Explanation / Important formulas:
Important formulas:
- km/hr to m/s conversion:
a km/hr = a x 5/18 m/s.
- m/s to km/hr conversion:
a m/s = a x 18/5 km/hr.
Formulas for finding Speed, Time and Distance:
- Time taken by a train of length l metres to pass a pole or standing man or a signal post is equal to the time taken by the train to cover l metres.
- Time taken by a train of length l metres to pass a stationery object of length b metres is the time taken by the train to cover (l + b) metres.
- Suppose two trains or two objects bodies are moving in the same direction at u m/s and v m/s, where u > v, then their relative speed is = (u – v) m/s.
- Suppose two trains or two objects bodies are moving in opposite directions at u m/s and v m/s, then their relative speed is = (u + v) m/s.
- If two trains of length a metres and b metres are moving in opposite directions at u m/s and v m/s, then:
The time taken by the trains to cross each other = (a + b) / (u + v) sec.
- If two trains of length a metres and b metres are moving in the same direction at u m/s and v m/s, then:
The time taken by the faster train to cross the slower train = (a + b) / (u -v) sec.
- If two trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then:
(A’s speed) : (B’s speed) = (b : a)
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Time, Work and Distance - Test
Time, Work and Distance - Question and Answers
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Question 1
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A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
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120 meters
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180 meters
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324 meters
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150 meters
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Question 1 Explanation:
Speed = (60 * 5/18) m/sec = (50/3) m/sec
Length of the train = (Speed * Time)
Length of the train = ((50/3) * 9) m = 150 m
Length of the train = (Speed * Time)
Length of the train = ((50/3) * 9) m = 150 m
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Question 2
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A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going in 10 seconds. The speed of the train is?
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45 km/hr
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54 km/hr
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50 km/hr
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55 km/hr
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Question 2 Explanation:
Speed of the train relative to man = 125/10 m/sec
=> 25/2 m/sec
=> 25/2 * 18/5 km/hr
=> 45 km/hr
Let the speed of the train be x km/hr
Then, relative speed = (x - 5) km/hr
=> x - 5 = 45
=> x = 50 km/hr
=> 25/2 m/sec
=> 25/2 * 18/5 km/hr
=> 45 km/hr
Let the speed of the train be x km/hr
Then, relative speed = (x - 5) km/hr
=> x - 5 = 45
=> x = 50 km/hr
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Question 3
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P is able to do a piece of work in 15 days and Q can do the same work in 20 days. If they can work together for 4 days, what is the fraction of work left?
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8/15
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7/15
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11/15
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2/11
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Question 3 Explanation:
Amount of work P can do in 1 day = 1/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 * (7/60) = 7/15
Fraction of work left = 1 – 7/15 = 8/15
Amount of work Q can do in 1 day = 1/20
Amount of work P and Q can do in 1 day = 1/15 + 1/20 = 7/60
Amount of work P and Q can together do in 4 days = 4 * (7/60) = 7/15
Fraction of work left = 1 – 7/15 = 8/15
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Question 4
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P can lay railway track between two stations in 16 days. Q can do the same job in 12 days. With the help of R, they completes the job in 4 days. How much days does it take for R alone to complete the work?
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9 (3/5) days
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9 (1/5) days
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9 (2/5) days
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10 days
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Question 4 Explanation:
Amount of work P can do in 1 day = 1/16
Amount of work Q can do in 1 day = 1/12
Amount of work P, Q and R can together do in 1 day = 1/4
Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48
=> Hence R can do the job on 48/5 days = 9 (3/5) days
Amount of work Q can do in 1 day = 1/12
Amount of work P, Q and R can together do in 1 day = 1/4
Amount of work R can do in 1 day = 1/4 - (1/16 + 1/12) = 3/16 – 1/12 = 5/48
=> Hence R can do the job on 48/5 days = 9 (3/5) days
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Question 5
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P, Q and R can do a work in 20, 30 and 60 days respectively. How many days does it. Need to complete the work if P does the work and he is assisted by Q and R on every third day?
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10 days
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14 days
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15 days
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9 days
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Question 5 Explanation:
Amount of work P can do in 1 day = 1/20
Amount of work Q can do in 1 day = 1/30
Amount of work R can do in 1 day = 1/60
P is working alone and every third day Q and R is helping him
Work completed in every three days = 2 * (1/20) + (1/20 + 1/30 + 1/60) = 1/5
So work completed in 15 days = 5 * 1/5 = 1
I.e, the work will be done in 15 days
Amount of work Q can do in 1 day = 1/30
Amount of work R can do in 1 day = 1/60
P is working alone and every third day Q and R is helping him
Work completed in every three days = 2 * (1/20) + (1/20 + 1/30 + 1/60) = 1/5
So work completed in 15 days = 5 * 1/5 = 1
I.e, the work will be done in 15 days
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Question 6
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A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in how many days if they work together?
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18 days
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22 1/2 days
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24 days
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26 days
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Question 6 Explanation:
If A completes a work in 1 day, B completes the same work in 3 days
Hence, if the difference is 2 days, B can complete the work in 3 days
=> if the difference is 60 days, B can complete the work in 90 days
=> Amount of work B can do in 1 day = 1/90
Amount of work A can do in 1 day = 3 * (1/90) = 1/30
Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45
=> A and B together can do the work in 45/2 days = 22 ½ days
Hence, if the difference is 2 days, B can complete the work in 3 days
=> if the difference is 60 days, B can complete the work in 90 days
=> Amount of work B can do in 1 day = 1/90
Amount of work A can do in 1 day = 3 * (1/90) = 1/30
Amount of work A and B can together do in 1 day = 1/90 + 1/30 = 4/90 = 2/45
=> A and B together can do the work in 45/2 days = 22 ½ days
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Question 7
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A can do a particular work in 6 days. B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?
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380
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600
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420
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400
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Question 7 Explanation:
Amount of work A can do in 1 day = 1/6
Amount of work B can do in 1 day = 1/8
Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work A + B + C can do = 1/3
Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24
Work A can do in 1 day : work B can do in 1 day : work C can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to C = 3200 * (1/8) = 400
Amount of work B can do in 1 day = 1/8
Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work A + B + C can do = 1/3
Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24
Work A can do in 1 day : work B can do in 1 day : work C can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to C = 3200 * (1/8) = 400
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Question 8
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6 men and 8 women can complete a work in 10 days. 26 men and 48 women can finish the same work in 2 days. 15 men and 20 women can do the same work in how many days?
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4 days
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6 days
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2 days
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8 days
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Question 8 Explanation:
Let work done by 1 man in 1 day = m and work done by 1 woman in 1 day = b
Work done by 6 men and 8 women in 1 day = 1/10
=> 6m + 8b = 1/10
=> 60m + 80b = 1 --- (1)
Work done by 26 men and 48 women in 1 day = 1/2
=> 26m + 48b = ½
=> 52m + 96b = 1--- (2)
Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200
Work done by 15 men and 20 women in 1 day
=> 15/100 + 20/200 = 1/4
=> Time taken by 15 men and 20 women in doing the work = 4 days
Work done by 6 men and 8 women in 1 day = 1/10
=> 6m + 8b = 1/10
=> 60m + 80b = 1 --- (1)
Work done by 26 men and 48 women in 1 day = 1/2
=> 26m + 48b = ½
=> 52m + 96b = 1--- (2)
Solving equation 1 and equation 2. We get m = 1/100 and b = 1/200
Work done by 15 men and 20 women in 1 day
=> 15/100 + 20/200 = 1/4
=> Time taken by 15 men and 20 women in doing the work = 4 days
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Question 9
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A can do a piece of work in 4 hours. A and C together can do it in just 2 hours, while B and C together need 3 hours to finish the same work. B alone can complete the work in how many hours?
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12 hours
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6 hours
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8 hours
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10 hours
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Question 9 Explanation:
Work done by A in 1 hour = 1/4
Work done by B and C in 1 hour = 1/3
Work done by A and C in 1 hour = 1/2
Work done by A,B and C in 1 hour = 1/4 + 1/3 = 7/12
Work done by B in 1 hour = 7/12 – 1/2 = 1/12
=> B alone can complete the work in 12 hours
Work done by B and C in 1 hour = 1/3
Work done by A and C in 1 hour = 1/2
Work done by A,B and C in 1 hour = 1/4 + 1/3 = 7/12
Work done by B in 1 hour = 7/12 – 1/2 = 1/12
=> B alone can complete the work in 12 hours
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Question 10
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P can do a work in the same time in which Q and R together can do it. If P and Q work together, the work can be completed in 10 days. R alone needs 50 days to complete the same work. then Q alone can do it in
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30 days
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25 days
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20 days
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15 days
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Question 10 Explanation:
Work done by P and Q in 1 day = 1/10
Work done by R in 1 day = 1/50
Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50
But Work done by P in 1 day = Work done by Q and R in 1 day
Hence the above equation can be written as
Work done by P in 1 day * 2 = 6/50
=> Work done by P in 1 day = 3/50
=> Work done by Q and R in 1 day = 3/50
Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25
So Q alone can do the work in 25 days
Work done by R in 1 day = 1/50
Work done by P, Q and R in 1 day = 1/10 + 1/50 = 6/50
But Work done by P in 1 day = Work done by Q and R in 1 day
Hence the above equation can be written as
Work done by P in 1 day * 2 = 6/50
=> Work done by P in 1 day = 3/50
=> Work done by Q and R in 1 day = 3/50
Hence work done by Q in 1 day = 3/50 – 1/50 = 2/50 = 1/25
So Q alone can do the work in 25 days
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Question 11
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A completes 80% of a work in 20 days. Then B also joins and A and B together finish the remaining work in 3 days. How long does it need for B if he alone completes the work?
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37 1/2 days
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22 days
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31 days
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27 days
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Question 11 Explanation:
Work done by A in 20 days = 80/100 = 8/10 = 4/5
Work done by A in 1 day = (4/5)/20 = 4/100 = 1/25 --- (1)
Work done by A and B in 3 days = 20/100 = 1/5
(Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 ---(2)
Work done by B in 1 day = 1/15 – 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 ½ days
Work done by A in 1 day = (4/5)/20 = 4/100 = 1/25 --- (1)
Work done by A and B in 3 days = 20/100 = 1/5
(Because remaining 20% is done in 3 days by A and B)
Work done by A and B in 1 day = 1/15 ---(2)
Work done by B in 1 day = 1/15 – 1/25 = 2/75
=> B can complete the work in 75/2 days = 37 ½ days
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Question 12
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Machine P can print one lakh books in 8 hours. Machine Q can print the same number of books in 10 hours while machine R can print the same in 12 hours. All the machines started printing at 9 A.M. Machine P is stopped at 11 A.M. and the remaining two machines complete work. Approximately at what time will the printing of one lakh books be completed?
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3 PM
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1PM
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11 AM
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2 PM
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Question 12 Explanation:
Work done by P in 1 hour = 1/8
Work done by Q in 1 hour = 1/10
Work done by R in 1 hour = 1/12
Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120
Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60
From 9 am to 11 am, all the machines were operating
i.e, they all operated for 2 hours and work completed = 2 * (37/120) = 37/60
Pending work = 1 - 37/60 = 23/60
Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11
which is approximately equal to 2
Hence the work will be completed approximately 2 hours after 11 am ; i.e. around 1 pm
Work done by Q in 1 hour = 1/10
Work done by R in 1 hour = 1/12
Work done by P,Q and R in 1 hour = 1/8 + 1/10 + 1/12 = 37/120
Work done by Q and R in 1 hour = 1/10 + 1/12 = 22/120 = 11/60
From 9 am to 11 am, all the machines were operating
i.e, they all operated for 2 hours and work completed = 2 * (37/120) = 37/60
Pending work = 1 - 37/60 = 23/60
Hours taken by Q an R to complete the pending work = (23/60) / (11/60) = 23/11
which is approximately equal to 2
Hence the work will be completed approximately 2 hours after 11 am ; i.e. around 1 pm
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Question 13
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P can finish a work in 18 days. Q can finish the same work in 15 days. Q worked for 10 days and left the job. how many days does P alone need to finish the remaining work?
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8
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5
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4
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6
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Question 13 Explanation:
Work done by P in 1 day = 1/18
Work done by Q in 1 day = 1/15
Work done by Q in 1 day = 1/15
Work done by Q in 10 days = 10/15 = 2/3
Remaining work = 1 – 2/3 = 1/3
Number of days in which P can finish the remaining work = (1/3) / (1/18) = 6
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Question 14
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3 men and 7 women can complete a work in 10 days. But 4 men and 6 women need 8 days to complete the same work. In how many days will 10 women complete the same work?
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50
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40
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30
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20
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Question 14 Explanation:
Work done by 4 men and 6 women in 1 day = 1/8
Work done by 3 men and 7 women in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day
The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 women can do in a day = 10 * (1/400) = 1/40
i.e, 10 women can complete the work in 40 days
Work done by 3 men and 7 women in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day
The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 women can do in a day = 10 * (1/400) = 1/40
i.e, 10 women can complete the work in 40 days
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Question 15
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A and B can finish a work 30 days if they work together. They worked together for 20 days and then B left. A finished the remaining work in another 20 days. In how many days A alone can finish the work?
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60
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50
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40
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30
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Question 15 Explanation:
Amount of work done by A and B in 1 day = 1/30
Amount of work done by A and B in 20 days = 20 *(1/30) = 20/30 = 2/3
Remaining work – 1– 2/3 = 1/3
A completes 1/3 work in 20 days
Amount of work A can do in 1 day = (1/3)/20 = 1/60
=> A can complete the work in 60 days
Amount of work done by A and B in 20 days = 20 *(1/30) = 20/30 = 2/3
Remaining work – 1– 2/3 = 1/3
A completes 1/3 work in 20 days
Amount of work A can do in 1 day = (1/3)/20 = 1/60
=> A can complete the work in 60 days
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Question 16
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A can complete a work in 12 days with a working of 8 hours per day. B can complete the same work in 8 days when working 10 hours a day. If A and B work together, working 8 hours a day, the work can be completed in how many days?
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5 5/11
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4 5/11
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6 4/11
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6 5/11
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Question 16 Explanation:
A can complete the work in 12 days working 8 hours a day
=> Number of hours A can complete the work = 12*8 = 96 hours
=> Work done by A in 1 hour = 1/96
B can complete the work in 8 days working 10 hours a day
=> Number of hours B can complete the work = 8*10 = 80 hours
=> Work done by B in 1 hour = 1/80
Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480
=> A and B can complete the work in 480/11 hours
A and B works 8 hours a day
Hence total days to complete the work with A and B working together
= (480/11)/ (8) = 60/11 days = 5 5 ⁄ 11 days
=> Number of hours A can complete the work = 12*8 = 96 hours
=> Work done by A in 1 hour = 1/96
B can complete the work in 8 days working 10 hours a day
=> Number of hours B can complete the work = 8*10 = 80 hours
=> Work done by B in 1 hour = 1/80
Work done by A and B in 1 hour = 1/96 + 1/80 = 11/480
=> A and B can complete the work in 480/11 hours
A and B works 8 hours a day
Hence total days to complete the work with A and B working together
= (480/11)/ (8) = 60/11 days = 5 5 ⁄ 11 days
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Question 17
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P is 30% more efficient than Q. P can complete a work in 23 days. If P and Q work together, how much time will it take to complete the same work?
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9
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11
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13
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15
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Question 17 Explanation:
Work done by P in 1 day = 1/23
Let work done by Q in 1 day = q
q * (130/100) = 1/23
=> q = 100 / (23*130) = 10 / (23*13)
Work done by P and Q in 1 day = 1/23 + 10 / (23*13) = 23 / (23*13) = 1/13
=> P and Q together can do the work in 13 days
Let work done by Q in 1 day = q
q * (130/100) = 1/23
=> q = 100 / (23*130) = 10 / (23*13)
Work done by P and Q in 1 day = 1/23 + 10 / (23*13) = 23 / (23*13) = 1/13
=> P and Q together can do the work in 13 days
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Question 18
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P, Q and R can complete a work in 24, 6 and 12 days respectively. The work will be completed in how many days if all of them are working together?
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2
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3 3/7
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4 1/4
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5
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Question 18 Explanation:
Work done by P in 1 day = 1/24
Work done by Q in 1 day = 1/6
Work done by R in 1 day = 1/12
Work done by P,Q and R in 1 day = 1/24 + 1/6 + 1/12 = 7/24
=> Working together, they will complete the work in 24/7 days = 3 3⁄7 days
Work done by Q in 1 day = 1/6
Work done by R in 1 day = 1/12
Work done by P,Q and R in 1 day = 1/24 + 1/6 + 1/12 = 7/24
=> Working together, they will complete the work in 24/7 days = 3 3⁄7 days
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Question 19
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10 men can complete a work in 7 days. But 10 women need 14 days to complete the same work. How many days will 5 men and 10 women need to complete the work?
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5
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6
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7
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8
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Question 19 Explanation:
Work done by 10 men in 1 day = 1/7
Work done by 1 man in 1 day = (1/7)/10 = 1/70
Work done by 1 man in 1 day = (1/7)/10 = 1/70
Work done by 10 women in 1 day = 1/14
Work done by 1 woman in 1 day = 1/140
Work done by 5 men and 10 women in 1 day = 5 × (1/70) + 10 × (1/140)
= 5/70 + 10/140 = 1/7
=> 5 men and 10 women can complete the work in 7 days
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Question 20
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Kamal will complete work in 20 days. If Suresh is 25% more efficient than Kamal, he can complete the work in how many days?
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14
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16
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18
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20
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Question 20 Explanation:
Work done by Kamal in 1 day = 1/20
Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16
=> Suresh can complete the work in 16 days
Work done by Suresh in 1 day = (1/20) × (125/100) = 5/80 = 1/16
=> Suresh can complete the work in 16 days
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Question 21
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Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 110 pages?
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7 hour 15 minutes
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7 hour 30 minutes
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8 hour 15 minutes
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8 hour 30 minutes
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Question 21 Explanation:
Pages typed by Anil in 1 hour = 32/6 = 16/3
Pages typed by Suresh in 1 hour = 40/5 = 8
Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3
Time taken to type 110 pages when Anil and Suresh work together = 110 * 3 /40 = 33/4
= 8 ¼ hours = 8 hour 15 minutes
Pages typed by Suresh in 1 hour = 40/5 = 8
Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3
Time taken to type 110 pages when Anil and Suresh work together = 110 * 3 /40 = 33/4
= 8 ¼ hours = 8 hour 15 minutes
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Question 22
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P and Q can complete a work in 20 days and 12 days respectively. P alone started the work and Q joined him after 4 days till the completion of the work. How long did the work last?
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5 days
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10 days
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14 days
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22 days
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Question 22 Explanation:
Work done by P in 1 day = 1/20
Work done by Q in 1 day = 1/12
Work done by P in 4 days = 4 × (1/20) = 1/5
Remaining work = 1 – 1/5 = 4/5
Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15
Number of days P and Q take to complete the remaining work = (4/5) / (2/15) = 6
Total days = 4 + 6 = 10
Work done by Q in 1 day = 1/12
Work done by P in 4 days = 4 × (1/20) = 1/5
Remaining work = 1 – 1/5 = 4/5
Work done by P and Q in 1 day = 1/20 + 1/12 = 8/60 = 2/15
Number of days P and Q take to complete the remaining work = (4/5) / (2/15) = 6
Total days = 4 + 6 = 10
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Question 23
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P takes twice as much time as Q or thrice as much time as R to finish a piece of work. They can finish the work in 2 days if work together. How much time will Q take to do the work alone?
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4
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|
5
|
|
|
6
|
|
|
7
|
Question 23 Explanation:
Let P takes x days to complete the work
Then Q takes x/2 days and R takes x/3 days to finish the work
Amount of work P does in 1 day = 1/x
Amount of work Q does in 1 day = 2/x
Amount of work R does in 1 day = 3/x
Amount of work P,Q and R do in 1 day = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x
6/x = 2
=> x = 12
=> Q takes 12/2 days = 6 days to complete the work
Then Q takes x/2 days and R takes x/3 days to finish the work
Amount of work P does in 1 day = 1/x
Amount of work Q does in 1 day = 2/x
Amount of work R does in 1 day = 3/x
Amount of work P,Q and R do in 1 day = 1/x + 2/x + 3/x = 1/x (1 + 2 + 3) = 6/x
6/x = 2
=> x = 12
=> Q takes 12/2 days = 6 days to complete the work
|
Question 24
|
P and Q can complete a work in 15 days and 10 days respectively. They started the work together and then Q left after 2 days. P alone completed the remaining work. The work was finished in how many days?
|
12
|
|
|
16
|
|
|
20
|
|
|
24
|
Question 24 Explanation:
Work done by P in 1 day = 1/15
Work done by Q in 1 day = 1/10
Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6
Work done by P and Q in 2 days = 2 * (1/6) = 1/3
Remaining work = 1 – 1/3 = 2/3
Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days
Total time taken = 2 + 10 = 12 days
Work done by Q in 1 day = 1/10
Work done by P and Q in 1 day = 1/15 + 1/10 = 1/6
Work done by P and Q in 2 days = 2 * (1/6) = 1/3
Remaining work = 1 – 1/3 = 2/3
Time taken by P to complete the remaining work 2/3 = (2/3) / (1/15) = 10 days
Total time taken = 2 + 10 = 12 days
|
Question 25
|
P and Q can do a work in 30 days. Q and R can do the same work in 24 days and R and P in 20 days. They started the work together, but Q and R left after 10 days. How many days more will P take to finish the work?
|
10
|
|
|
15
|
|
|
18
|
|
|
22
|
Question 25 Explanation:
Let work done by P in 1 day = p
Work done by Q in 1 day = q
Work done by R in 1 day = r
p + q = 1/30
q + r = 1/24
r + p = 1/20
Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8
=> p + q + r = 1/16
=> Work done by P,Q and R in 1 day = 1/16
Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8
Remaining work = 1 = 5/8 = 3/8
Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day
= 1/16 – 1/24 = 1/48
Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18
Work done by Q in 1 day = q
Work done by R in 1 day = r
p + q = 1/30
q + r = 1/24
r + p = 1/20
Adding all the above, 2p + 2q + 2r = 1/30 + 1/24+ 1/20 = 15/120 = 1/8
=> p + q + r = 1/16
=> Work done by P,Q and R in 1 day = 1/16
Work done by P, Q and R in 10 days = 10 × (1/16) = 10/16 = 5/8
Remaining work = 1 = 5/8 = 3/8
Work done by P in 1 day = Work done by P,Q and R in 1 day - Work done by Q and R in 1 day
= 1/16 – 1/24 = 1/48
Number of days P needs to work to complete the remaining work = (3/8) / (1/48) = 18
|
Question 26
|
P works twice as fast as Q. If Q alone can complete a work in 12 days,
P and Q can finish the work in how many days?
P and Q can finish the work in how many days?
|
1
|
|
|
2
|
|
|
3
|
|
|
4
|
Question 26 Explanation:
Work done by Q in 1 day = 1/12
Work done by P in 1 day = 2 * (1/12) = 1/6
Work done by P in 1 day = 2 * (1/12) = 1/6
Work done by P and Q in 1 day = 1/12 + 1/6 = ¼
=> P and Q can finish the work in 4 days
|
Question 27
|
A work can be finished in 16 days by twenty women. The same work can be finished in fifteen days by sixteen men. The ratio between the capacity of a man and a woman is?
|
1:3
|
|
|
4:3
|
|
|
2:3
|
|
|
2:1
|
Question 27 Explanation:
Work done by 20 women in 1 day = 1/16
Work done by 1 woman in 1 day = 1/(16*20)
Work done by 16 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15*16)
Ratio of the capacity of a man and woman =1/(15*16) : 1/(16*20) = 1/15 : 1/20
= 1/3 :1/4 = 4:3
Work done by 1 woman in 1 day = 1/(16*20)
Work done by 16 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15*16)
Ratio of the capacity of a man and woman =1/(15*16) : 1/(16*20) = 1/15 : 1/20
= 1/3 :1/4 = 4:3
|
Question 28
|
P and Q need 8 days to complete a work. Q and R need 12 days to complete the same work. But P, Q and R together can finish it in 6 days. How many days will be needed if P and R together do it?
|
3
|
|
|
8
|
|
|
12
|
|
|
4
|
Question 28 Explanation:
Let work done by P in 1 day = p
work done by Q in 1 day = q
Work done by R in 1 day = r
p + q = 1/8 ---(1)
q + r = 1/12 ---(2)
p + q + r = 1/6 ---(3)
(3) – (2) => p = 1/6 - 1/12 = 1/12
(3) – (1) => r = 1/6 – 1/8 = 1/24
p + r = 1/12 + 1/24 = 3/24 = 1/8
=> P and R will finish the work in 8 days
work done by Q in 1 day = q
Work done by R in 1 day = r
p + q = 1/8 ---(1)
q + r = 1/12 ---(2)
p + q + r = 1/6 ---(3)
(3) – (2) => p = 1/6 - 1/12 = 1/12
(3) – (1) => r = 1/6 – 1/8 = 1/24
p + r = 1/12 + 1/24 = 3/24 = 1/8
=> P and R will finish the work in 8 days
|
Question 29
|
P can do a work in 24 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in how many days?
|
7
|
|
|
8
|
|
|
9
|
|
|
10
|
Question 29 Explanation:
Work done by P in 1 day = 1/24
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3*7/36 = 7/12
Remaining work = 1 – 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/24) = 10
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3*7/36 = 7/12
Remaining work = 1 – 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/24) = 10
|
Question 30
|
If daily wages of a man is double to that of a woman, how many men should work for 25 days to earn Rs.14400? Given that wages for 40 women for 30 days are Rs.21600?
|
12
|
|
|
14
|
|
|
16
|
|
|
18
|
Question 30 Explanation:
Wages of 1 woman for 1 day = 2160040*30
Wages of 1 man for 1 day = 21600×240*30
Wages of 1 man for 25 days = 21600*2*2540*30
Number of men = 14400(21600*2*2540*30) = 144(216*5040*30) = 1449 = 16
Wages of 1 man for 1 day = 21600×240*30
Wages of 1 man for 25 days = 21600*2*2540*30
Number of men = 14400(21600*2*2540*30) = 144(216*5040*30) = 1449 = 16
|
Question 31
|
P,Q and R together earn Rs.1620 in 9 days. P and R can earn Rs.600 in 5 days. Q and R in 7 days can earn Rs.910. How much amount does R can earn per day?
|
Rs. 40
|
|
|
Rs. 70
|
|
|
Rs. 90
|
|
|
Rs. 100
|
Question 31 Explanation:
Amount Earned by P,Q and R in 1 day = 1620/9 = 180 ---(1)
Amount Earned by P and R in 1 day = 600/5 = 120 ---(2)
Amount Earned by Q and R in 1 day = 910/7 = 130 ---(3)
(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day
Amount Earned by P,Q and R in 1 day = 120+130-180 = 70
=> Amount Earned by R in 1 day = 70
Amount Earned by P and R in 1 day = 600/5 = 120 ---(2)
Amount Earned by Q and R in 1 day = 910/7 = 130 ---(3)
(2)+(3)-(1) => Amount Earned by P , Q and 2R in 1 day
Amount Earned by P,Q and R in 1 day = 120+130-180 = 70
=> Amount Earned by R in 1 day = 70
|
Question 32
|
Assume that 20 cows and 40 goats can be kept for 10 days for Rs.460. If the cost of keeping 5 goats is the same as the cost of keeping 1 cow, what will be the cost for keeping 50 cows and 30 goats for 12 days?
|
Rs. 1104
|
|
|
Rs. 1000
|
|
|
Rs. 934
|
|
|
Rs. 1210
|
Question 32 Explanation:
Assume that cost of keeping a cow for 1 day = c ,
cost of keeping a goat for 1 day = g
Cost of keeping 20 cows and 40 goats for 10 days = 460
Cost of keeping 20 cows and 40 goats for 1 day = 460/10 = 46
=> 20c + 40g = 46
=> 10c + 20g = 23 ---(1)
Given that 5g = c
Hence equation (1) can be written as 10c + 4c = 23 => 14c =23
=> c = 23/14
cost of keeping 50 cows and 30 goats for 1 day
= 50c + 30g
= 50c + 6c (substituted 5g = c)
= 56 c = 56*23/14
= 92
Cost of keeping 50 cows and 30 goats for 12 days = 12*92 = 1104
cost of keeping a goat for 1 day = g
Cost of keeping 20 cows and 40 goats for 10 days = 460
Cost of keeping 20 cows and 40 goats for 1 day = 460/10 = 46
=> 20c + 40g = 46
=> 10c + 20g = 23 ---(1)
Given that 5g = c
Hence equation (1) can be written as 10c + 4c = 23 => 14c =23
=> c = 23/14
cost of keeping 50 cows and 30 goats for 1 day
= 50c + 30g
= 50c + 6c (substituted 5g = c)
= 56 c = 56*23/14
= 92
Cost of keeping 50 cows and 30 goats for 12 days = 12*92 = 1104
|
Question 33
|
There is a group of people, each of whom can complete a piece of work in 16 days, when they are working individually. On the first day one person works, on the second day another person joins him, on the third day one more person joins them and this process continues till the work is completed. How many days are needed to complete the work?
|
3 1⁄4 days
|
|
|
4 1⁄3 days
|
|
|
5 1⁄6 days
|
|
|
6 1⁄5 days
|
Question 33 Explanation:
Work completed in 1st day = 1/16
Work completed in 2nd day = (1/16) + (1/16) = 2/16
Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16
An easy way to attack such problems is from the choices. You can see the choices are
very close to each other. So just see one by one
For instance, The first choice given in 3 1⁄4
The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16
The work done in 4 days = (1+2+3+4)/16 = 10/16
The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn't it?
The work done in 6 days = (1+2+3+4+5+6)/16 > 1
Hence the answer is less than 6, but greater than 5
Hence the answer is 5 1⁄6 days
(Just for your reference, work done in 5 days = 15/16
Pending work in 6th day = 1 – 15/16 = 1/16
In 6th day, 6 people are working and work done = 6/16
To complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days
Hence total time required = 5 + 1/6 = 5 1⁄6 days
Work completed in 2nd day = (1/16) + (1/16) = 2/16
Work completed in 3rd day = (1/16) + (1/16) + (1/16) = 3/16
An easy way to attack such problems is from the choices. You can see the choices are
very close to each other. So just see one by one
For instance, The first choice given in 3 1⁄4
The work done in 3 days = 1/16 + 2/16 + 3/16 = (1+2+3)/16 = 6/16
The work done in 4 days = (1+2+3+4)/16 = 10/16
The work done in 5 days = (1+2+3+4+5)/16 = 15/16, almost close, isn't it?
The work done in 6 days = (1+2+3+4+5+6)/16 > 1
Hence the answer is less than 6, but greater than 5
Hence the answer is 5 1⁄6 days
(Just for your reference, work done in 5 days = 15/16
Pending work in 6th day = 1 – 15/16 = 1/16
In 6th day, 6 people are working and work done = 6/16
To complete the work 1/16, time required = (1/16) / (6/16) = 1/6 days
Hence total time required = 5 + 1/6 = 5 1⁄6 days
|
Question 34
|
Riya and priya set on a journey. Riya moves eastward at a speed of 20km/h and priya moves westward at a speed of 30km/h. How far will be priya from riya after 30 min?
|
25 km
|
|
|
10 km
|
|
|
50 km
|
|
|
30 km
|
Question 34 Explanation:
Distance = relative speed * time
= (20+15) * 1/2
=25
= (20+15) * 1/2
=25
|
Question 35
|
A man takes 5 hours 45 min in walking to a certain place and riding back. He would have gained 2 hours by riding both ways. The time he would take to walk both ways is?
|
11 hrs
|
|
|
8 hrs 45 min
|
|
|
7 hrs 45 min
|
|
|
9 hrs 20 min
|
Question 35 Explanation:
Given that time taken for riding both ways will be 2 hours lesser than the time needed for waking one way and riding back
From this, we can understand that time needed for
riding one way = time needed for waking one way - 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min
From this, we can understand that time needed for
riding one way = time needed for waking one way - 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min
|
Question 36
|
Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
|
12
|
|
|
11
|
|
|
10
|
|
|
9
|
Question 36 Explanation:
Due to stoppages, it covers 9 km less
Time taken to cover 9 km = (9/54 * 60) min = 10 min
Time taken to cover 9 km = (9/54 * 60) min = 10 min
|
Question 37
|
A man complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km/hr and second half at the rate of 24 km/hr. Find the total journey in km?
|
121
|
|
|
242
|
|
|
224
|
|
|
112
|
Question 37 Explanation:
(1/2)x /21 + (1/2)x /24 = 10
x/21 + x/24 = 20
15x = 168 * 20
x = (168 * 20 / 15) = 224 km
x/21 + x/24 = 20
15x = 168 * 20
x = (168 * 20 / 15) = 224 km
|
Question 38
|
A car traveling with 5/7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. What is the actual speed of the car?
|
30 km/hr
|
|
|
35 km/hr
|
|
|
25 km/hr
|
|
|
40 km/hr
|
Question 38 Explanation:
Time taken = 1 hr 40 min 48 sec = 1 hr 40 4/5 min = 1 51/75 hrs = 126/75 hrs
Let the actual speed be x km/hr
Then, 5/7x * 126/75 = 42
x = (42 * 7 * 75/5 * 126) = 35 km/hr
Let the actual speed be x km/hr
Then, 5/7x * 126/75 = 42
x = (42 * 7 * 75/5 * 126) = 35 km/hr
|
Question 39
|
A man covered a certain distance at some speed. If he had moved 3 kmph faster, he would have taken 40 minutes less. If he had moved 2 kmph slower, he would have taken 40 minutes more. What is the the distance in km?
|
36
|
|
|
38
|
|
|
40
|
|
|
42
|
Question 39 Explanation:
Let distance = x km and usual rate = y kmph
Then, x/y – x /(y+3) = 40/60 => 2y(y+3) = 9x ….(1)
And, x/(y-2) – x/y = 40/60 => y(y-2) = 3x ………(2)
On dividing (1) by (2), we get x = 40
Then, x/y – x /(y+3) = 40/60 => 2y(y+3) = 9x ….(1)
And, x/(y-2) – x/y = 40/60 => y(y-2) = 3x ………(2)
On dividing (1) by (2), we get x = 40
|
Question 40
|
A and B walk around a circular track. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. If they start at 8 a.m. from the same point in opposite directions, how many times shall they cross each other before 9.30 a.m.?
|
5
|
|
|
6
|
|
|
7
|
|
|
8
|
Question 40 Explanation:
Relative speed = Speed of A + Speed of B (∴ they walk in opposite directions)
= 2 + 3 = 5 rounds per hour
=> They cross each other 5 times in 1 hour and 2 times in 1/2 hour
Time duration from 8 am to 9.30 am = 1.5 hour
Hence they cross each other 7 times before 9.30 am
= 2 + 3 = 5 rounds per hour
=> They cross each other 5 times in 1 hour and 2 times in 1/2 hour
Time duration from 8 am to 9.30 am = 1.5 hour
Hence they cross each other 7 times before 9.30 am
|
Question 41
|
Two boys starts from the same place walking at the rate of 5 kmph and 5.5 kmph respectively in the same direction. What time will they take to be 8.5 km apart?
|
17 hr
|
|
|
14 hr
|
|
|
12 hr
|
|
|
19 hr
|
Question 41 Explanation:
Relative speed = 5.5 - 5 = 0.5 kmph (because they walk in the same direction)
Distance = 8.5 km
Time = Distance * Speed = 8.5 * 0.5 = 17 hr
Distance = 8.5 km
Time = Distance * Speed = 8.5 * 0.5 = 17 hr
|
Question 42
|
In covering a distance of 30 km, Arun takes 2 hours more than Anil. If Arun doubles his speed, then he would take 1 hour less than Anil. What is Arun's speed?
|
8 kmph
|
|
|
5 kmph
|
|
|
4 kmph
|
|
|
7 kmph
|
Question 42 Explanation:
Let Abhay's speed be x km/hr
Then, 30/x – 30/2x = 3
6x = 30
x = 5 km/hr
Then, 30/x – 30/2x = 3
6x = 30
x = 5 km/hr
|
Question 43
|
A car travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. What is the average speed for the first 320 km of the tour?
|
70.24 km/hr
|
|
|
74. 24 km/hr
|
|
|
71.11 km/hr
|
|
|
72.21 km/hr
|
Question 43 Explanation:
We know time = Distance/speed
So, total time taken = (160/64 + 160/80) = 9/2 hours
Time taken for 320 km = 320 * 2/9 = 71.11
= 71.11 km/hr
So, total time taken = (160/64 + 160/80) = 9/2 hours
Time taken for 320 km = 320 * 2/9 = 71.11
= 71.11 km/hr
|
Question 44
|
A Man travelled a distance of 61 km in 9 hours. He travelled partly on foot at 4 km/hr and partly on bicycle at 9 km/hr. What is the distance travelled on foot?
|
12 km
|
|
|
14 km
|
|
|
16 km
|
|
|
18 km
|
Question 44 Explanation:
let the distance he travelled on foot = x km
Then the distance he travelled on bicycle = (61-x) km
So, x/4 + (61−x)/9 = 9
9x + 4(61−x) = 9 * 36
5x= 80
x = 16 km
Then the distance he travelled on bicycle = (61-x) km
So, x/4 + (61−x)/9 = 9
9x + 4(61−x) = 9 * 36
5x= 80
x = 16 km
|
Question 45
|
Walking 6/7th of his usual speed, a man is 12 minutes too late. What is the usual time taken by him to cover that distance?
|
1 hr 42 min
|
|
|
1 hr
|
|
|
2 hr
|
|
|
1 hr 12 min
|
Question 45 Explanation:
New speed = 6/7 of usual speed
Speed and time are inversely proportional
Hence new time = 7/6 of usual time
Hence, 7/6 of usual time - usual time = 12 minutes
=> 1/6 of usual time = 12 minutes
=> usual time = 12 * 6 = 72 minutes
=> 1 hour 12 minutes
Speed and time are inversely proportional
Hence new time = 7/6 of usual time
Hence, 7/6 of usual time - usual time = 12 minutes
=> 1/6 of usual time = 12 minutes
=> usual time = 12 * 6 = 72 minutes
=> 1 hour 12 minutes
|
Question 46
|
A man goes to his office from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming, what is the distance between his house and office?
|
3 km
|
|
|
4 km
|
|
|
5 km
|
|
|
6 km
|
Question 46 Explanation:
If a car covers a certain distance at x kmph and
An Equal distance at y kmph, the average speed of the whole journey = 2xy/x+y kmph
Hence, average speed = (2*3*2) /2+3 = 12/5 km/hr
Total time taken = 5 hours
⇒ Distance travelled = 12/5*5 = 12 km
⇒ Distance between his house and office = 12/2 = 6 km
An Equal distance at y kmph, the average speed of the whole journey = 2xy/x+y kmph
Hence, average speed = (2*3*2) /2+3 = 12/5 km/hr
Total time taken = 5 hours
⇒ Distance travelled = 12/5*5 = 12 km
⇒ Distance between his house and office = 12/2 = 6 km
|
Question 47
|
A man rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. What is his average speed for the entire trip approximately?
|
11.2 kmph
|
|
|
10 kmph
|
|
|
10.2 kmph
|
|
|
10.8 kmph
|
Question 47 Explanation:
Total distance travelled = (10 + 12)km = 22 km
Time taken to travel 10 km at an average speed of 12 km/hr = distance * speed = 10/12 hr
Time taken to travel 12 km at an average speed of 10 km/hr = distance * speed = 12/10 hr
Total time taken = [10/12 + 12/10] hr = 61/30 hrs
Average speed = [22*30/61] km/hr = 10.8 km/hr
Time taken to travel 10 km at an average speed of 12 km/hr = distance * speed = 10/12 hr
Time taken to travel 12 km at an average speed of 10 km/hr = distance * speed = 12/10 hr
Total time taken = [10/12 + 12/10] hr = 61/30 hrs
Average speed = [22*30/61] km/hr = 10.8 km/hr
|
Question 48
|
An airplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of?
|
660 km/hr
|
|
|
680 km/hr
|
|
|
700 km/hr
|
|
|
720 km/hr
|
Question 48 Explanation:
Distance = (240 * 5) = 1200 km
Speed = Distance/Time
Speed = 1200 / (5/3) km/hr
Therefore required speed = (1200 * 3/5) km/hr
= 720 km/hr
Speed = Distance/Time
Speed = 1200 / (5/3) km/hr
Therefore required speed = (1200 * 3/5) km/hr
= 720 km/hr
|
Question 49
|
A train can travel 50% faster than a car. Both start from point A at the same time and reach point B 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. What is the speed of the car?
|
80 kmph
|
|
|
102 kmph
|
|
|
120 kmph
|
|
|
140 kmph
|
Question 49 Explanation:
Let speed of the car be x kmph
Then, speed of the train = 150/100x = (3/2x) kmph
75/x - 75/(3/2)x = 125/10 * 60
75/x – 50/x = 5/24
x = (25 * 24 / 5) = 120 kmph
Then, speed of the train = 150/100x = (3/2x) kmph
75/x - 75/(3/2)x = 125/10 * 60
75/x – 50/x = 5/24
x = (25 * 24 / 5) = 120 kmph
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Question 50
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In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. What is the duration of the flight?
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2 hour
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112 hour
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12 hour
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1 hour
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Question 50 Explanation:
Let the duration of the flight be x hours
Then, 600/x – 600/x + (1/2) = 200
600/x – 1200/2x + 1 = 200
x(2x + 1) = 3
2*2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr [neglecting the -ve value of x]
Then, 600/x – 600/x + (1/2) = 200
600/x – 1200/2x + 1 = 200
x(2x + 1) = 3
2*2 + x - 3 = 0
(2x + 3)(x - 1) = 0
x = 1 hr [neglecting the -ve value of x]
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Question 51
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If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. What is the actual distance travelled by him?
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80 km
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70 km
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60 km
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50 km
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Question 51 Explanation:
Let the actual distance travelled be x km
Then, x / 10 = x+20 / 14
14x = 10x + 200
4x = 200
x = 50 km
Then, x / 10 = x+20 / 14
14x = 10x + 200
4x = 200
x = 50 km
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Question 52
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The ratio between the speeds of two trains is 7:8. If the second train runs 400 km in 4 hours, What is the the speed of the first train?
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85 km/hr
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87.5 km/hr
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90 km/hr
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92.5 km/hr
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Question 52 Explanation:
Let the speed of two trains be 7x and 8x km/hr
Then, 8x = 400/4) = 100
x = (100/8) = 12.5
Speed of first train = (7 * 12.5) km/hr = 87.5 km/hr
Then, 8x = 400/4) = 100
x = (100/8) = 12.5
Speed of first train = (7 * 12.5) km/hr = 87.5 km/hr
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Question 53
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A car travels at an average of 50 miles per hour for 212 hours and then travels at a speed of 70 miles per hour for 112 hours. How far did the car travel in the entire 4 hours?
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210 miles
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230 miles
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250 miles
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260 miles
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Question 53 Explanation:
Speed1 = 50 miles/hour
Time1 = 212 hour = 52 Hour
Distance1 = Speed1 × Time1
=> 50 × 52 = 25 × 5 = 125 Miles
Speed2 = 70 miles/hour
Time2 = 112 hour = 32 hour
Distance2 = Speed2 × Time2 = 70*32 = 35*3 = 105 miles
Total Distance = Distance1 + Distance2
= 125 + 105 = 230 miles
Time1 = 212 hour = 52 Hour
Distance1 = Speed1 × Time1
=> 50 × 52 = 25 × 5 = 125 Miles
Speed2 = 70 miles/hour
Time2 = 112 hour = 32 hour
Distance2 = Speed2 × Time2 = 70*32 = 35*3 = 105 miles
Total Distance = Distance1 + Distance2
= 125 + 105 = 230 miles
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Question 54
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The speed of a bus increases by 2 km after every one hour. If the distance travelling in the first one hour was 35 km. what was the total distance travelled in 12 hours?
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422 km
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552 km
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502 km
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492 km
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Question 54 Explanation:
Given that distance travelled in 1st hour = 35 km
And speed of the bus increases by 2 km after every one hour
Hence distance travelled in 2nd hour = 37 km
Hence distance travelled in 3rd hour = 39 km
Total Distance Travelled = [35 + 37 + 39 + ... (12 terms)]
This is an Arithmetic Progression(AP) with
first term, a = 35, number of terms ,n = 12 and common difference, d = 2
The sequence a , (a + d), (a + 2d), (a + 3d), (a + 4d), . .
. is called an Arithmetic Progression(AP)where a is the first term and d is the common difference of the AP
Sum of the first n terms of an Arithmetic Progression(AP),
Sn=n2[2a+(n−1)d]where n = number of terms
Hence, [35+37+39+... (12 terms)] = S12 = 122[2*35+(12−1)2] = 6[70+22] = 6 * 92 = 552
Hence the total distance travelled = 552 km
And speed of the bus increases by 2 km after every one hour
Hence distance travelled in 2nd hour = 37 km
Hence distance travelled in 3rd hour = 39 km
Total Distance Travelled = [35 + 37 + 39 + ... (12 terms)]
This is an Arithmetic Progression(AP) with
first term, a = 35, number of terms ,n = 12 and common difference, d = 2
The sequence a , (a + d), (a + 2d), (a + 3d), (a + 4d), . .
. is called an Arithmetic Progression(AP)where a is the first term and d is the common difference of the AP
Sum of the first n terms of an Arithmetic Progression(AP),
Sn=n2[2a+(n−1)d]where n = number of terms
Hence, [35+37+39+... (12 terms)] = S12 = 122[2*35+(12−1)2] = 6[70+22] = 6 * 92 = 552
Hence the total distance travelled = 552 km
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Question 55
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Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5 seconds after he sees it strike the tree.How far is the man from the wood chopper?
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1800 ft
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2810 ft
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3020 ft
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2420 ft
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Question 55 Explanation:
Speed of the sound = 1100 ft/s
Time = 11/5 second
Distance = Speed * Time = 1100 *115 = 220*11 = 2420 ft
Time = 11/5 second
Distance = Speed * Time = 1100 *115 = 220*11 = 2420 ft
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Question 56
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The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travel towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 Km/hr. At what time will they meet?
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10.30 a.m
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10 a.m.
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12 noon
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11 a.m.
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Question 56 Explanation:
Assume that they meet x hours after 8 a.m
Then, train1, starting from A , travelling towards B, travels x hours till the trains meet
⇒ Distance travelled by train1 in x hours = Speed *Time = 60x
Then, train2, starting from B , travelling towards A, travels (x-1) hours till the trains meet
⇒ Distance travelled by train2 in (x-1) hours = Speed *Time = 75(x-1)
Total distance travelled = Distance travelled by train1 + Distance travelled by train2
=> 330 = 60x + 75(x-1)
=> 12x + 15(x-1) = 66
=> 12x + 15x - 15 = 66
=> 27x = 66 + 15 = 81
=> 3x = 9
=> x = 3
Hence the trains meet 3 hours after 8 a.m., i.e. at 11 a.m
Then, train1, starting from A , travelling towards B, travels x hours till the trains meet
⇒ Distance travelled by train1 in x hours = Speed *Time = 60x
Then, train2, starting from B , travelling towards A, travels (x-1) hours till the trains meet
⇒ Distance travelled by train2 in (x-1) hours = Speed *Time = 75(x-1)
Total distance travelled = Distance travelled by train1 + Distance travelled by train2
=> 330 = 60x + 75(x-1)
=> 12x + 15(x-1) = 66
=> 12x + 15x - 15 = 66
=> 27x = 66 + 15 = 81
=> 3x = 9
=> x = 3
Hence the trains meet 3 hours after 8 a.m., i.e. at 11 a.m
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Question 57
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A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. What is the length of the bridge (in metres)?
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1250
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1280
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1320
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1340
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Question 57 Explanation:
We need to get the answer in meters
So we will first of change distance from km/hour to meter/sec by multiplying it with 5/18 and also change 15 minutes to seconds by multiplying it with 60
Speed = 5*5/18 = 25/18 m/sec
Time = 15 * 60 seconds = 900 seconds
Distance = Time * Speed
Distance = (25 / 18) * 900 = 1250 meter
So we will first of change distance from km/hour to meter/sec by multiplying it with 5/18 and also change 15 minutes to seconds by multiplying it with 60
Speed = 5*5/18 = 25/18 m/sec
Time = 15 * 60 seconds = 900 seconds
Distance = Time * Speed
Distance = (25 / 18) * 900 = 1250 meter
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Question 58
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A train travelled at an average speed of 100 km/hr, stopping for 3 minutes after every 75 km. How long did it take to reach its destination 600 km from the starting point?
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6 hrs 21 min
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7 hrs 14 min
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7 hrs 22 min
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6 hrs
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Question 58 Explanation:
Average Speed = 100 km/hr
With this speed, train can cover 600 km in 6 hours but train used to stop for 3 minutes after every 75 km
So, Train will stop = 600/75 = 8 times in the whole journey
But, you need to understand that after 7th stopping train will be at the destiny in next stop. Therefore, train will stop 7 times in journey
So, extra time = 7 *3 = 21 minutes
Total time taken in the journey = 6 hour 21 minutes
With this speed, train can cover 600 km in 6 hours but train used to stop for 3 minutes after every 75 km
So, Train will stop = 600/75 = 8 times in the whole journey
But, you need to understand that after 7th stopping train will be at the destiny in next stop. Therefore, train will stop 7 times in journey
So, extra time = 7 *3 = 21 minutes
Total time taken in the journey = 6 hour 21 minutes
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Question 59
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A person travels from A to B at a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?
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60 km/hr
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56 km/hr
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52 km/hr
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48 km/hr
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Question 59 Explanation:
Speed while going = 40 km/hr
Speed while returning = 150% 0f 40 = 60 km/hr
Average speed = 2xy/x+y
= (2*40*60/40+60)
= 4800/100 = 48 km/hr
Speed while returning = 150% 0f 40 = 60 km/hr
Average speed = 2xy/x+y
= (2*40*60/40+60)
= 4800/100 = 48 km/hr
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Question 60
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A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
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3.6
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7.2
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8.4
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10
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Question 60 Explanation:
Speed = [600 / (5*60)] m/sec = 2 m / sec
(Converting m/sec to km/hr (see important formulas section)
= [2* (18 / 5)] km/hr
= 7.2 km/hr
(Converting m/sec to km/hr (see important formulas section)
= [2* (18 / 5)] km/hr
= 7.2 km/hr
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Question 61
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If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is?
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50 km
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80 km
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70 km
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90 km
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Question 61 Explanation:
Let the actual distance travelled be x km
x / 10 = x + 20/14
14x = 10x + 200
4x = 200
x = 50 km
x / 10 = x + 20/14
14x = 10x + 200
4x = 200
x = 50 km
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Question 62
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It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. What is the ratio of the speed of the train to that of the car?
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3 : 4
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2 : 3
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1 : 2
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1 : 3
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Question 62 Explanation:
Let the speed of the train be x km/hr and that of the car be y km/hr
Then, 120/x + 480/y = 8 => 1/x + 4/y = 1/15 …..(1)
And, 200/x + 400/y = 25/3 => 1/x +2/y =1/24 …..(2)
Solving (1) and (2), we get x = 60 and y = 80
Ratio of speeds = 60 : 80 = 3 : 4
Then, 120/x + 480/y = 8 => 1/x + 4/y = 1/15 …..(1)
And, 200/x + 400/y = 25/3 => 1/x +2/y =1/24 …..(2)
Solving (1) and (2), we get x = 60 and y = 80
Ratio of speeds = 60 : 80 = 3 : 4
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Question 63
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Arun is traveling on his cycle and has calculated to reach point A at 2 pm if he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 pm?
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8 kmph
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10 kmph
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12 kmph
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14 kmph
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Question 63 Explanation:
Let the distance travelled be x km
Then, x/10 – x/15 = 2
= 3x - 2x = 60 => x = 60 km
Time taken to travel 60 km at 10 km/hr = (60/10)hrs = 6 hrs
So, Arun started 6 hours before 2 P.M i.e.., at 8 A.M
Therefore Required speed = (60/5)kmph = 12 kmph
Then, x/10 – x/15 = 2
= 3x - 2x = 60 => x = 60 km
Time taken to travel 60 km at 10 km/hr = (60/10)hrs = 6 hrs
So, Arun started 6 hours before 2 P.M i.e.., at 8 A.M
Therefore Required speed = (60/5)kmph = 12 kmph
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Question 64
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An athlete runs 200 meters race in 24 seconds. What is his speed?
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20 km/hr
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25 km/hr
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27.5 km/hr
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30 km/hr
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Question 64 Explanation:
Speed = Distance/Time = 200/24 m/s
=> 200/24*185 km/hr
=> 40*34 km/hr = 10*3 km/hr = 30 km/hr
=> 200/24*185 km/hr
=> 40*34 km/hr = 10*3 km/hr = 30 km/hr
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Question 65
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A train is moving at the speed of 80 km/hr. What is its speed in meters per second?
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2229 m/s
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22 m/s
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2119 m/sec
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21 m/s
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Question 65 Explanation:
Speed = 80 km/hr = 80*5/18 m/s
=> 40×59 m/s = 2009 m/s
=> 2229 m/s
=> 40×59 m/s = 2009 m/s
=> 2229 m/s
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Question 66
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A man in a train notices that he can count 21 telephone posts in one minute. If they are known to be 50 metres apart, at what speed is the train travelling?
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61 km/hr
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56 km/hr
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63 km/hr
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60 km/hr
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Question 66 Explanation:
Number of poles = 21
Distance between them = 50m
Total distance = 20*50m = 1000m = 1 km
Time taken is = 1min = 1/60 hr
Speed = Distance / time
Speed = 1/(1/60) = 1*60 = 60 kmph
Distance between them = 50m
Total distance = 20*50m = 1000m = 1 km
Time taken is = 1min = 1/60 hr
Speed = Distance / time
Speed = 1/(1/60) = 1*60 = 60 kmph
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Question 67
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A truck covers a distance of 550 metres in 1 minute whereas a train covers a distance of 33 kms in 45 minutes. What is the ratio of their speed?
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2 : 1
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1 : 2
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4 : 3
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3 : 4
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Question 67 Explanation:
Ratio of speeds = (550/60 * 18/5) : (33/45 * 60)
= 33 : 44 = 3 : 4
= 33 : 44 = 3 : 4
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Question 68
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A person has to cover a distance of 6 km in 45 minutes. If he covers one-half of the distance in two-thirds of the total time; to cover the remaining distance in the remaining time, what should be his speed in km/hr?
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14 km/hr
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12 km/hr
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10 km/hr
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8 km/hr
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Question 68 Explanation:
The person needs to cover 6 km in 45 minutes
Given that he covers one-half of the distance in two-thirds of the total time
He covers half of 6 km in two-thirds of 45 minutes
He covers 3 km in 30 minutes
Hence, now he need to cover the remaining 3 km in the remaining 15 minutes
Distance = 3 km
Time = 15 minutes = 1/4 hour
Required Speed = Distance/Time = 3/(1/4) = 12 km/hr
Given that he covers one-half of the distance in two-thirds of the total time
He covers half of 6 km in two-thirds of 45 minutes
He covers 3 km in 30 minutes
Hence, now he need to cover the remaining 3 km in the remaining 15 minutes
Distance = 3 km
Time = 15 minutes = 1/4 hour
Required Speed = Distance/Time = 3/(1/4) = 12 km/hr
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Question 69
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An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 1 2/3 hours, it must travel at a speed of?
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300 kmph
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360 kmph
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600 kmph
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720 kmph
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Question 69 Explanation:
Distance = (240 x 5) = 1200 km
Speed = Distance/Time
Speed = 1200 / (5/3) km/hr [We can write 1 2/3 hours as 5/3 hours]
Therefore required speed = (1200 * 3/5) km/hr = 720 km/hr
Speed = Distance/Time
Speed = 1200 / (5/3) km/hr [We can write 1 2/3 hours as 5/3 hours]
Therefore required speed = (1200 * 3/5) km/hr = 720 km/hr
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Question 70
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Robert is travelling on his cycle and has calculated to reach point A at 2 P.M. If he travels at 10 kmph, he will reach there at 12 noon if he travels at 15 kmph. At what speed must he travel to reach A at 1 P.M?
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8 kmph
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11 kmph
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12 kmph
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14 kmph
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Question 70 Explanation:
Let the distance travelled by x km
Then, x/10 – x/15 = 2
3x – 2x = 60
x = 60 km
Time taken to travel 60 km at 10 km/hr = (60/10)hrs = 6 hrs
So, Robert started 6 hours before 2 P.M
i.e., at 8 A.M
Therefore, Required speed = (60/5) kmph = 12 kmph
Then, x/10 – x/15 = 2
3x – 2x = 60
x = 60 km
Time taken to travel 60 km at 10 km/hr = (60/10)hrs = 6 hrs
So, Robert started 6 hours before 2 P.M
i.e., at 8 A.M
Therefore, Required speed = (60/5) kmph = 12 kmph
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Question 71
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A farmer travelled a distance of 61 km in 9 hours. He travelled partly on foot @ 4 km/hr and partly on bicycle @ 9 km/hr. The distance travelled on foot is?
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14 km
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15 km
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16 km
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17 km
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Question 71 Explanation:
Let the distance travelled on foot be x km
Then, distance travelled on bicycle = (61 -x) km
So, x / 4 + (61-x) / 9 = 9
9x + 4(61-x) = 9 * 36
5x = 80
x = 16 km
Then, distance travelled on bicycle = (61 -x) km
So, x / 4 + (61-x) / 9 = 9
9x + 4(61-x) = 9 * 36
5x = 80
x = 16 km
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Question 72
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A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is?
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35.55 km/hr
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36 km/hr
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71.11 km/hr
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71 km/hr
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Question 72 Explanation:
Total time taken = (160/64 + 160/80) hrs = 9/2 hrs
Average speed = (320 * 2/9) km/hr = 71.11 km/hr
Average speed = (320 * 2/9) km/hr = 71.11 km/hr
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