Explanation / Important formulas:
Direct Proportion:
- Two quantities are said to be directly proportional, if on the increase (or decrease) of the one, the other increases (or decreases) to the same extent.
Example: Cost is directly proportional to the number of articles. (More Articles, More Cost)
Indirect Proportion:
Two quantities are said to be indirectly proportional, if on the increase of the one, the other decreases to the same extent and vice-versa.
Example: The time taken by a car is covering a certain distance is inversely proportional to the speed of the car. (More speed, less is the time taken to cover a distance).
Note: In solving problems by chain rule, we compare every item with the term to be found out
Instructions to take Aptitude Test
- Click on start to start taking the test.
- Click on the option (A, B, C or D) to figure out the right answer.
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- On click of question number you will go to that particular question.
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Test - Chain Rule
Chain rule - Question and Answers
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Question 1
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If 36 men can do a piece of work in 25 hours, in how many hours will 15 men do it?
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A
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20 hours
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B
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60 hours
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C
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80 hours
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D
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70 hours
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Question 1 Explanation:
Let the required number of hours be x.
Less man, more hours (indirect proportion)
15:36:: 25: x
15 * x = 36 * 25
X= (36 *25) / 15 = 60 hours
Hence 15 men’s can do it in 60 hours
Less man, more hours (indirect proportion)
15:36:: 25: x
15 * x = 36 * 25
X= (36 *25) / 15 = 60 hours
Hence 15 men’s can do it in 60 hours
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Question 2
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If the wages of 6 men for 15 days be Rs.2100, then the wages of 9 men for 12 days?
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A
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Rs. 2520
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B
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Rs. 3065
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C
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Rs. 7658
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D
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Rs 2765
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Question 2 Explanation:
Let the required wages be x
More men, more wages( Direct proportion)
Less days, Less wages ( Direct proportion)
Men = 6:9 ::2100 😡
Days = 15:12 :: 2100 : x
(6*15*x) = (9* 12* 2100)
X = [(9*12*2100) / (6* 15)]
X = 420 * 6
X= 2520
Hence, the required wages are Rs. 2520
More men, more wages( Direct proportion)
Less days, Less wages ( Direct proportion)
Men = 6:9 ::2100 😡
Days = 15:12 :: 2100 : x
(6*15*x) = (9* 12* 2100)
X = [(9*12*2100) / (6* 15)]
X = 420 * 6
X= 2520
Hence, the required wages are Rs. 2520
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Question 3
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8 children and 12 men complete a certain piece of work in 9 days. If each child takes twice the time taken by a man to finish the work, in how many days will 12 men finish the same work?
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A
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16 days
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B
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12 days
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C
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22 days
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D
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26 days
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Question 3 Explanation:
2 children = 1 man
(8 children + 12 men) = 16 men
Less men, more days( Indirect proportion )
12 : 16 :: 9: x
12x= (16*9)
12x = 144
X= 144/12
X= 12 days
(8 children + 12 men) = 16 men
Less men, more days( Indirect proportion )
12 : 16 :: 9: x
12x= (16*9)
12x = 144
X= 144/12
X= 12 days
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Question 4
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Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minutes. At this rate, how many bottles could 10 such machines produce in 4 minutes?
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A
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1500
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B
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1600
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C
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1800
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D
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1964
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Question 4 Explanation:
Let the required number of bottles be x
More machines, more bottles(direct proportion)
Machines = 6: 10 ::270 : x
Time(in minutes) = 1:4 :: 270 : x
6 * 1* x= 10* 4* 270
X= (10*4*270) / (6*1)
= 20 * 90
X = 1800
More machines, more bottles(direct proportion)
Machines = 6: 10 ::270 : x
Time(in minutes) = 1:4 :: 270 : x
6 * 1* x= 10* 4* 270
X= (10*4*270) / (6*1)
= 20 * 90
X = 1800
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Question 5
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4 mat weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat weavers in 8 days?
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A
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16
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B
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17
Hint:
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C
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19
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D
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64
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Question 5 Explanation:
Let the required number of mats be x
More mat weavers, more mats(Direct proportion)
More days, more mats ( Direct proportion)
Mat weavers = 4:8 :: 4 : x
Days = 4:8 :: 4:x
4*4*x=8*8*4
X= (8*8*4) / (4*4)
X= 2*2*4
X= 16
More mat weavers, more mats(Direct proportion)
More days, more mats ( Direct proportion)
Mat weavers = 4:8 :: 4 : x
Days = 4:8 :: 4:x
4*4*x=8*8*4
X= (8*8*4) / (4*4)
X= 2*2*4
X= 16
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Question 6
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If a quarter kg of potato coasts 60 paise, how many paise will 200 gm cost?
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A
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87
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B
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56
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C
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48
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D
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65
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Question 6 Explanation:
Let the required weight be x kg
Less weight, less cost (Direct proportion)
250 : 200 :: 60 : x
250 * x = (200 * 60)
X= (200 * 60) / 250
X= 8*6
X= 48
Less weight, less cost (Direct proportion)
250 : 200 :: 60 : x
250 * x = (200 * 60)
X= (200 * 60) / 250
X= 8*6
X= 48
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Question 7
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In a hospital there is a consumption of 1350 liters of milk for 70patients for 30 days. How many patients will consume 1710 litres of milk in 28 days?
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A
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100 patients
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B
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120 patients
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C
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95 patients
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D
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140 patients
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Question 7 Explanation:
Let the required number of number be x
= More liters, more patients (Direct proportion)
=Less days, more patients (Indirect proportion)
Litres = 1350: 1710: : 70 : x
Days = 20: 8::70: x
X= (1710*30*70) / (1350 * 28)
= 19 * 5
95 patients
= More liters, more patients (Direct proportion)
=Less days, more patients (Indirect proportion)
Litres = 1350: 1710: : 70 : x
Days = 20: 8::70: x
X= (1710*30*70) / (1350 * 28)
= 19 * 5
95 patients
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Question 8
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39 person can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours day, complete the work?
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A
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13 days
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B
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27 days
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C
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17 days
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D
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18 days
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Question 8 Explanation:
Let the required number of days be x
Less persons, More days(Indirect proportion)
More working hours per day, Less days(Indirect proportion)
Person = 30:39 ::12 : x
Working hours/days = 6: 5 ::12 : x
(30*6*x)= (39*5*12)
X= (39*5*12) / (30*6)
X= 13 days
Less persons, More days(Indirect proportion)
More working hours per day, Less days(Indirect proportion)
Person = 30:39 ::12 : x
Working hours/days = 6: 5 ::12 : x
(30*6*x)= (39*5*12)
X= (39*5*12) / (30*6)
X= 13 days
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Question 9
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If 20 men working together can finish a job in 20 days, then the number of days taken by 25 men of the same capacity to finish the job is?
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A
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25
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B
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16
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C
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20
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D
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12
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Question 9 Explanation:
25:20:: 20: x or 25x= 20 * 20
Or = [20*20/25] = 16
Required number of days = 16
Or = [20*20/25] = 16
Required number of days = 16
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Question 10
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If 16 men working 7 hours day can plough a field in 4l days, in how many days will 14 men working 12 hours clay plough the same field?
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A
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46
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B
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32
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C
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35
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D
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30
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Question 10 Explanation:
(Men 14:16): (Hrs/Day 12: 7) :: 48 : x
14*12* x = 16* 7 * 48 or x= 32
14*12* x = 16* 7 * 48 or x= 32
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Question 11
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Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in?
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A
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6 days
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B
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12 days
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C
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3 days
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D
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4 days
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Question 11 Explanation:
(Men 2x: x): (work 1:1/2):: 12 :y
2x *1 * y = x* ½ *12 or y = 3
2x *1 * y = x* ½ *12 or y = 3
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Question 12
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A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many ends does the wheel move in 1 hour?
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A
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2000
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B
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1200
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C
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600
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D
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12000
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Question 12 Explanation:
Answer: Option C
Number of wheel moves in 1 hour = 10 * 60 = 600
Distance moved = 600 * 200 = 12000
Number of wheel moves in 1 hour = 10 * 60 = 600
Distance moved = 600 * 200 = 12000
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Question 13
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If 10 men’s can reap a field in 8 days, then 8 men will reap the same field in?
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A
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5 days
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B
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4 days
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C
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10 days
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D
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20 days
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Question 13 Explanation:
8: 10 :: 8: x
Or 8x = 10 * 8
Or x= 10
Required number of days 10
Or 8x = 10 * 8
Or x= 10
Required number of days 10
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Question 14
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If 18 persons can build a wall 140m long in 42 days, the number of days that 30 persons will take to complete a similar wall 100 m long, is?
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A
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18
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B
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24
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C
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21
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D
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28
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Question 14 Explanation:
(Length 140:100) : (Persons 30:18) : : 42 : x
140 * 30 * x = 100 * 18 * 42
Or x= 18
140 * 30 * x = 100 * 18 * 42
Or x= 18
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Question 15
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The price of 438 oranges is Rs. 1384.08. What will be the approximate price of 8 dozens of oranges?
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A
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300
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B
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400
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C
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500
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D
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250
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Question 15 Explanation:
438:96:: 1384.08 : x
Or x= 96 * 1384.08 / 438 = 303.36
Approx cost = Rs. 300
Or x= 96 * 1384.08 / 438 = 303.36
Approx cost = Rs. 300
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Question 16
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If 12 carpenters, working 6 hours a day can make 460 chairs in 24 days, how many chairs will 18 carpenters make in 36 days, each working 8 hours a day?
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A
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1260
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B
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920
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C
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1320
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D
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1380
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Question 16 Explanation:
(Carpenters 12:18) : (His/Day 6:8) : (Days 24: 36) :: 460 : x
12*6 * 24*x = 18 * 8* 36* 460
Or x= 1380
12*6 * 24*x = 18 * 8* 36* 460
Or x= 1380
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Question 17
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The price of 357 mangoes is Rs. 1517.25. What will be the approximate price of 49 dozen of such mangoes?
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A
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Rs. 3000
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B
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Rs. 4000
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C
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Rs. 3500
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D
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Rs. 2500
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Question 17 Explanation:
More mangoes, more cost (Direct)
357: 49 * 12:: 1517.25 : x
Or 375* x= 49 * 12 * 1517.25
49* 12 * 15|7.25 / 357 = 2499
Approximate cost = Rs. 2500
357: 49 * 12:: 1517.25 : x
Or 375* x= 49 * 12 * 1517.25
49* 12 * 15|7.25 / 357 = 2499
Approximate cost = Rs. 2500
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Question 18
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If 15 toys cost Rs. 234, what do 35 toys cost?
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A
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486
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B
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546
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C
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626
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D
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686
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Question 18 Explanation:
Let the required cost be Rs. x
Then, more toys, more cost(Direct proportion)
15: 35:: 234 : x
(15 x x) = (35 x 234)
X= (35 X 234) / 15 = 546
Hence, the cost of 35 toys is Rs. 546
Then, more toys, more cost(Direct proportion)
15: 35:: 234 : x
(15 x x) = (35 x 234)
X= (35 X 234) / 15 = 546
Hence, the cost of 35 toys is Rs. 546
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Question 19
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If 36 men can do a piece of work in 25 hours, in how many hours will 15men do it?
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A
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40 hrs
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B
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50 hrs
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C
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60 hrs
|
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D
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70 hrs
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Question 19 Explanation:
Let the required number of hours be x
Then, less men, more hours(Indirect proportion)
15:36 :: 25 : x
(15 X x) = (36 X 25)
(36 X 25)/15 = 60
Hence, 15 men can do it in 60 hours
Then, less men, more hours(Indirect proportion)
15:36 :: 25 : x
(15 X x) = (36 X 25)
(36 X 25)/15 = 60
Hence, 15 men can do it in 60 hours
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Question 20
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If the wages of 6 men for 15 days be Rs. 200, then the wages of for 12 days?
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A
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2200
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B
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2520
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C
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2720
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D
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3000
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Question 20 Explanation:
Let the required wages be Rs. x
More men, more wages (Direct proportion)
Less days, less wages (Direct proportion)
Men 6:9:: 2100: x
Days 15:12
Therefore (16 x 15 x X) = (9 x 12 x 2100)
X= (9 x 12 x 2100) / (6 x 15) = 2520
Hence the required wages are Rs. 2520
More men, more wages (Direct proportion)
Less days, less wages (Direct proportion)
Men 6:9:: 2100: x
Days 15:12
Therefore (16 x 15 x X) = (9 x 12 x 2100)
X= (9 x 12 x 2100) / (6 x 15) = 2520
Hence the required wages are Rs. 2520
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Question 21
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If 20 men can build a wall 66 meters long in 6 days, what length of a similar can be built by 86men in 8 days?
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A
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44 m
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B
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49 m
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C
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54 m
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D
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59 m
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Question 21 Explanation:
Let the required length be x meters
More men, more length built (Direct proportion)
Less days, less length built (Direct proportion)
Men 20:35
Days 6:3:: 56: x
Therefore (20 x 6 x X) = (35 x 3x 56)
X= (35 x 3x 56) / 120 = 49
Hence, the required length is 49 m
More men, more length built (Direct proportion)
Less days, less length built (Direct proportion)
Men 20:35
Days 6:3:: 56: x
Therefore (20 x 6 x X) = (35 x 3x 56)
X= (35 x 3x 56) / 120 = 49
Hence, the required length is 49 m
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Question 22
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If 15 men, working 9 hours a day, can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day?
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A
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19
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B
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12
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C
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15
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D
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18
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Question 22 Explanation:
Let the required number of days be x
More men, less days (Indirect proportion)
Less hours per day, more days (Indirect proportion)
Men 18:15
Hours per day 8:9 :: 16 : x
(18 x 8 x X) = (15 x 9 x 16)
X = (44 x 15)144 = 15
Hence, the required number of days = 15
More men, less days (Indirect proportion)
Less hours per day, more days (Indirect proportion)
Men 18:15
Hours per day 8:9 :: 16 : x
(18 x 8 x X) = (15 x 9 x 16)
X = (44 x 15)144 = 15
Hence, the required number of days = 15
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Question 23
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If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?
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A
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1
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B
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3
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C
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7
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D
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14
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Question 23 Explanation:
Answer: Option C
Let the required number days be x
Less spider, More days (Indirect proportion)
Less webs, less days (Direct Proportion)
1 x7 x X = 7 x 1 x 7
X = 7
Let the required number days be x
Less spider, More days (Indirect proportion)
Less webs, less days (Direct Proportion)
1 x7 x X = 7 x 1 x 7
X = 7
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Question 24
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If 9 engines consume 24 metric tonnes of coal, when each is working 8 hours a day, how much coal will be required for 8 engines, each running 13 hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type?
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A
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22 metric tonnes
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B
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24 metric tonnes
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C
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26 metric tonnes
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D
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28 metric tonnes
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Question 24 Explanation:
Let 3engines of former type consume 1 unit in 1 hour
Then, 4 engines of latter type consume 1 unit in 1 hour
Therefore 1 engine of former type consumes (1/3) unit in 1 hour
1 engine of latter type consumes (1/4) unit in 1 hour
Let the required consumption of coal be x units
Less engines, less coal consumed (Direct proportion)
More working hours, more coal consumed (Direct proportion)
Less rate of consumption, less coal consumed(Direct proportion)
Number of engines 9:8
Working hours 8: 13:: 24 : x
Rate of consumption (1/3) : (1/4)
[9x8x(1/3)x X] = (8 x 13 x (1/4) x 24)
24x = 624
X= 26
Hence, the required consumption of coal= 26metric tonnes
Then, 4 engines of latter type consume 1 unit in 1 hour
Therefore 1 engine of former type consumes (1/3) unit in 1 hour
1 engine of latter type consumes (1/4) unit in 1 hour
Let the required consumption of coal be x units
Less engines, less coal consumed (Direct proportion)
More working hours, more coal consumed (Direct proportion)
Less rate of consumption, less coal consumed(Direct proportion)
Number of engines 9:8
Working hours 8: 13:: 24 : x
Rate of consumption (1/3) : (1/4)
[9x8x(1/3)x X] = (8 x 13 x (1/4) x 24)
24x = 624
X= 26
Hence, the required consumption of coal= 26metric tonnes
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Question 25
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A garrison of 3300 men had provisions for 32 days, when given at the rate of 860 gms per head. At the end of 7 days, reinforcement arrives and it was for that the provisions will last 17 days more, when given at the rate of 826 gms per head, what is the strength of the reinforcement?
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A
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1500
|
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B
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1700
|
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C
|
1900
|
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D
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2100
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Question 25 Explanation:
The problem becomes:
3300 men taking 850 gms per head have provisions for(32 - 7) or 25 days
How many men taking 825 gms each have provisions for 17 days?
Less ration per head, more men(Indirect proportion)
Less days, more men(Indirect proportion)
Ratio 825: 850
Days 17 :25 ::3300 : x
(825 x 17 x X) = 850 x 25 x 3300
Or x= (850 x 25 x 3300) / (825 x 17) = 5000
Strength of reinforcement = (5500 - 3300) = 1700
3300 men taking 850 gms per head have provisions for(32 - 7) or 25 days
How many men taking 825 gms each have provisions for 17 days?
Less ration per head, more men(Indirect proportion)
Less days, more men(Indirect proportion)
Ratio 825: 850
Days 17 :25 ::3300 : x
(825 x 17 x X) = 850 x 25 x 3300
Or x= (850 x 25 x 3300) / (825 x 17) = 5000
Strength of reinforcement = (5500 - 3300) = 1700
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Question 26
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36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
|
A
|
12
|
|
B
|
18
|
|
C
|
22
|
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D
|
24
|
Question 26 Explanation:
Let the required number of days be x
Less man, more days (Indirect proportion)
27 :36 ::18 : x 27 X x = 36 x
X =36 x 18/27
X= 24
Less man, more days (Indirect proportion)
27 :36 ::18 : x 27 X x = 36 x
X =36 x 18/27
X= 24
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Question 27
|
If a quarter kg of potato costs 60 paise, how many paise will 200 gm cost?
|
A
|
48 paise
|
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B
|
54 paise
|
|
C
|
56 paise
|
|
D
|
72 paise
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Question 27 Explanation:
Let the required weight be x kg
Less weight, less cost (Direct proportion) 250:200::60: x 250 x
X= (200 x 60)
X= (200 x 60) /250
X= 48
Less weight, less cost (Direct proportion) 250:200::60: x 250 x
X= (200 x 60)
X= (200 x 60) /250
X= 48
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Question 28
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If cost of x meters of wire is d rupees, then what is the cost of y meters of wire at the same rate?
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A
|
Rs. (xy/d)
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|
B
|
Rs. (xd)
|
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C
|
Rs.(yd)
|
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D
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Rs. (yd/x)
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Question 28 Explanation:
Cost of x meter = Rs. d
Cost of 1 meter = Rs.(d/x)
Cost of y meters = Rs.[(d/x).y] = Rs.(yd/x)
Cost of 1 meter = Rs.(d/x)
Cost of y meters = Rs.[(d/x).y] = Rs.(yd/x)
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Question 29
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39 Persons can repair a road in 12 days, working 5 hours day. In how many days will 30 persons, working 6 hours a day, complete the work?
|
A
|
10
|
|
B
|
13
|
|
C
|
14
|
|
D
|
15
|
Question 29 Explanation:
Let the required number of days be x
Less persons, more days (Indirect proportion)
More working hours per day, less days (Indirect proportion)
30 x 6 x X = 39 x 5 x12
X= 13
Less persons, more days (Indirect proportion)
More working hours per day, less days (Indirect proportion)
30 x 6 x X = 39 x 5 x12
X= 13
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Question 30
|
In a cam, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
|
A
|
50
|
|
B
|
40
|
|
C
|
30
|
|
D
|
20
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Question 30 Explanation:
There is a meal for 200 children. 150 children have taken the meal. Remaining meal is to be catered to 50 children.
Now , 200 children = 120 men
50 children = 30 men
Now , 200 children = 120 men
50 children = 30 men
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Question 31
|
A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the beginning and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?
|
A
|
3
|
|
B
|
5
|
|
C
|
6
|
|
D
|
9
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Question 31 Explanation:
4500 men can finish the work in 1day. 100 men can finish it in = 45 days
This is 5 days behind schedule
This is 5 days behind schedule
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Question 32
|
If a cloth merchant sells ‘a’ meter of cloth for Rs.x, then what is the selling price of ‘b’ meters of cloth?
|
A
|
Rs.(b*x)
|
|
B
|
Rs. {(b*x)/a}
|
|
C
|
Rs.{(a*b)/x}
|
|
D
|
none of these
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Question 32 Explanation:
Cost of ‘a’ meters of cloth = Rs. x
Therefore, each meter of cloth costs Rs. (x/a).
The cost of ‘b’ meters of cloth = Rs. b*(x/a) = Rs. {(b*x)/a}
Therefore, each meter of cloth costs Rs. (x/a).
The cost of ‘b’ meters of cloth = Rs. b*(x/a) = Rs. {(b*x)/a}
|
Question 33
|
A military camp has a food reserve for 250 personnel for 40 days. If after 15 days 50 more personnel are added to the camp, find the number of days the reserve will last for?
|
A
|
20
|
|
B
|
36
|
|
C
|
25
|
|
D
|
42
|
Question 33 Explanation:
As the camp has a reserve for 250 personnel that can last for 40 days, after 10 days the reserve left for 250 personnel is for 30 days.
Now 50 more personnel are added in the camp. hence, the food reserve for 300 personnel will last for:
250:300:: x:30 ...(It is an indirect proportion as less men means more days)
X= (250*30)/300
X= 25 days
Now 50 more personnel are added in the camp. hence, the food reserve for 300 personnel will last for:
250:300:: x:30 ...(It is an indirect proportion as less men means more days)
X= (250*30)/300
X= 25 days
|
Question 34
|
A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 28 adults have their meal, find the total number of children that can be catered with the remaining food.
|
A
|
42
|
|
B
|
54
|
|
C
|
90
|
|
D
|
70
|
Question 34 Explanation:
As there is meal for 70 adults and 28 have their meal, the meal left can be catered to 42 adults.
Now, 70 adults = 90 children
7 adult = 9 children
Therefore, 42 adults = 54 children
Hence, the meal can be catered to 54 children
Now, 70 adults = 90 children
7 adult = 9 children
Therefore, 42 adults = 54 children
Hence, the meal can be catered to 54 children
|
Question 35
|
If a carpenter completes 3/8th of his work in 6 days, then how many more days will he require completing his remaining work?
|
A
|
10
|
|
B
|
12
|
|
C
|
6
|
|
D
|
16
|
Question 35 Explanation:
As 3/8th of the work is completed, the work remaining is 58th of the total.
(3/8):6:: (5/8):x
X= 6*(5/8) / (3/8)
X= 10
(3/8):6:: (5/8):x
X= 6*(5/8) / (3/8)
X= 10
|
Question 36
|
If a certain number of people can dig earth 100m deep, 25m long, and 30m broad in 12days, then find the number of people will required to dig earth 75m deep, 20m long and 50m broad?
|
A
|
12
|
|
B
|
18
|
|
C
|
6
|
|
D
|
1
|
Question 36 Explanation:
More number of days means – more length, more depth and more width.
Hence it’s a direct proportion.
(100*25*30): (75*20*50):: 12 😡
75000:75000:: 12:x
X = 12
Hence it’s a direct proportion.
(100*25*30): (75*20*50):: 12 😡
75000:75000:: 12:x
X = 12
|
Question 37
|
For a road work, a contractor was given a deadline to complete the work in 25 days. Hence, he employed a certain number of workers to accomplish the job. But from the very first day 9 workers were absent and the remaining workers could finish the work in 40 days. What number of workers did the contractor hired in the beginning?
|
A
|
20
|
|
B
|
30
|
|
C
|
24
|
|
D
|
16
|
Question 37 Explanation:
Let the number of workers initially hired be x
Hence, x workers can complete the work in 25 days and (x-9) workers can complete the work in 40 days
Now, the number of men and the amount of work are in direct proportion and number of men and number of days in indirect proportion
X*25 = (x -9)*40
25x=40x – 360
15x=360
X=24
Hence, x workers can complete the work in 25 days and (x-9) workers can complete the work in 40 days
Now, the number of men and the amount of work are in direct proportion and number of men and number of days in indirect proportion
X*25 = (x -9)*40
25x=40x – 360
15x=360
X=24
|
Question 38
|
If 10 men can do a certain amount of work in 24days, then in how many days can 20 men complete half the amount of work?
|
A
|
12
|
|
B
|
24
|
|
C
|
6
|
|
D
|
18
|
Question 38 Explanation:
M1D1W2 = M2D2W1
10*24*W1/2 = 20* D2*W1...... (W2=W1 / 2)
D2 = 6 days
10*24*W1/2 = 20* D2*W1...... (W2=W1 / 2)
D2 = 6 days
|
Question 39
|
In how many days can 4 men and 4 women complete a certain work, if 2 men or 6 women can complete the same work in 12days?
|
A
|
4.5
|
|
B
|
6
|
|
C
|
12
|
|
D
|
4
|
Question 39 Explanation:
2men = 6women
Hence, 4 men = 12 women
4 men and 4 women = 12 + 4 = 16 women
M1 D1 W2= M2 D2 W1
M1 D1 = M2 D2 ....(W1 = W2)
6*12 = 16*D2
D2 = 4.5 day
Hence, 4 men = 12 women
4 men and 4 women = 12 + 4 = 16 women
M1 D1 W2= M2 D2 W1
M1 D1 = M2 D2 ....(W1 = W2)
6*12 = 16*D2
D2 = 4.5 day
|
Question 40
|
A two stored building is to be completed in 48 days. To meet the deadline 54 men were employed and were made to work for 10 hours a day. After 30 days 5/9th of the work was completed. How many more workers should be employed to meet the deadline if each workers are now made to work 8 hours a day?
|
A
|
36
|
|
B
|
90
|
|
C
|
40
|
|
D
|
50
|
Question 40 Explanation:
54men work 10 hours a day for 30 days and 5/9th of the work is completed
Now, let x workers be employed to work 8 hours a day for the rest 18 days to complete 4/9th of the work
M1 D1 T1 W2 = M2 D2 T2 W1
54*30*10*4/9 = x*18* 8*5/9
X= 90
Hence, 36 more workers should be employed
Now, let x workers be employed to work 8 hours a day for the rest 18 days to complete 4/9th of the work
M1 D1 T1 W2 = M2 D2 T2 W1
54*30*10*4/9 = x*18* 8*5/9
X= 90
Hence, 36 more workers should be employed
|
Question 41
|
If the cost of x meters of wire is d rupees, then what is the cost of y meters of wire at the same rate?
|
A
|
Rs. (xd/y)
|
|
B
|
Rs. xd
|
|
C
|
Rs.(yd/x)
|
|
D
|
Rs. yd
|
Question 41 Explanation:
Cost of x meters of wire = Rs. d
Cost of 1 meter of wire= Rs.(d/x)
Cost of y meter of wire = Rs. (y*dx) = Rs. (yd/x)
Cost of 1 meter of wire= Rs.(d/x)
Cost of y meter of wire = Rs. (y*dx) = Rs. (yd/x)
|
Question 42
|
In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with remaining meal?
|
A
|
50
|
|
B
|
30
|
|
C
|
40
|
|
D
|
10
|
Question 42 Explanation:
Meal for 200 children = Meal for 120 men
Meal for 1 child = Meal for 120/200 men
Meal for 150 children = Meal for 120 x 150/200 men = Meal for 90 men
Total meal available = meal for 120 men
Remaining meal = Meal for 120 men – Meal for 90 men = Meal for 30 men
Meal for 1 child = Meal for 120/200 men
Meal for 150 children = Meal for 120 x 150/200 men = Meal for 90 men
Total meal available = meal for 120 men
Remaining meal = Meal for 120 men – Meal for 90 men = Meal for 30 men
|
Question 43
|
If a quarter kg of potato costs 60 paise, how many paise dos 200 gm cost/
|
A
|
65 paise
|
|
B
|
70 paise
|
|
C
|
52 paise
|
|
D
|
48 paise
|
Question 43 Explanation:
Let 200 gm potato costs x paise
Cost of ¼ kg potato = 60 paise
Cost of 250gm potato = 60 paise
More quantity, more prise
Hence we can write as
Quality(200:250)::x:60
200 x 60 = 250 x X
4 x 60 = 5 x X
4 x 12 = X
X= 48
Cost of ¼ kg potato = 60 paise
Cost of 250gm potato = 60 paise
More quantity, more prise
Hence we can write as
Quality(200:250)::x:60
200 x 60 = 250 x X
4 x 60 = 5 x X
4 x 12 = X
X= 48
|
Question 44
|
A wheel that has 6 cogs is meshed with a large wheel of 14 cogs. If the smaller wheel has made 21 revolutions, what will be the number of revolutions made by the large wheel?
|
A
|
15
|
|
B
|
12
|
|
C
|
21
|
|
D
|
9
|
Question 44 Explanation:
Let the number of revolutions made by the larger wheel be x
More cogs, less revolutions (indirect proportion)
Hence we can write as
Cogs(6:14)::x:21
6 x 21 = 14 x X
6 x 3 = 2 x X
3 x 3 = X
X= 9
More cogs, less revolutions (indirect proportion)
Hence we can write as
Cogs(6:14)::x:21
6 x 21 = 14 x X
6 x 3 = 2 x X
3 x 3 = X
X= 9
|
Question 45
|
A certain industrial loom weaves 0.128 meters of cloth every second. Approximately how many seconds will it take for the loom to weave 25 meters of cloth?
|
A
|
205
|
|
B
|
200
|
|
C
|
195
|
|
D
|
190
|
Question 45 Explanation:
Let the required number of second be x
More cloth, more time,(direct proportion)
Hence we can write as
Cloth 0.128:25}:: 1: x
0.128x= 25
X= 25/128 = 25000/128
= 3125/16 = 195
More cloth, more time,(direct proportion)
Hence we can write as
Cloth 0.128:25}:: 1: x
0.128x= 25
X= 25/128 = 25000/128
= 3125/16 = 195
|
Question 46
|
21 goats eat as much as 15 cows. How many goats eat as much as 35 cows?
|
A
|
49
|
|
B
|
36
|
|
C
|
50
|
|
D
|
41
|
Question 46 Explanation:
15 cows = 21 goats
1 cow = 21/15 goats
35 cows
= 21 x 35/15 goats = 21 x 7/3 goats = 7 x 7 goats
= 49 goats
1 cow = 21/15 goats
35 cows
= 21 x 35/15 goats = 21 x 7/3 goats = 7 x 7 goats
= 49 goats
|
Question 47
|
A flagstaff 17.5 m high casts a shadow of length 40.25m.what will be the height of a building, which casts a shadow of length 28.75m under similar conditions?
|
A
|
12.5 m
|
|
B
|
10.5 m
|
|
C
|
14
|
|
D
|
12
|
Question 47 Explanation:
Let the required height of the building be x meter
More shadow length, more height
Hence we can write as
Shadow length {40.25:28.75}:: 17.5 : x
40.25x X = 28.75 x 17.5
X= 28.75 x17.5/40.25
2875 x 7/1610
2875/230
575/46
12.5
More shadow length, more height
Hence we can write as
Shadow length {40.25:28.75}:: 17.5 : x
40.25x X = 28.75 x 17.5
X= 28.75 x17.5/40.25
2875 x 7/1610
2875/230
575/46
12.5
|
Question 48
|
A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. Find out the number of days for which the remaining food will last?
|
A
|
44
|
|
B
|
42
|
|
C
|
36
|
|
D
|
52
|
Question 48 Explanation:
Given that the fort had provision of food for 150 men for 45 days
Hence, after 10 days, the remaining food is sufficient for 150 men for 35 days
Remaining men after 10 days =150 – 25 = 125
Assume that after 10 days, the remaining food is sufficient for 125 men for x days
More men, less days
Men {150:125}:: x:35
150 x 35 = 125x=> 6x35= 5x=>x = 6x7 = 42
The remaining food is sufficient for 125 men for 42 days
Hence, after 10 days, the remaining food is sufficient for 150 men for 35 days
Remaining men after 10 days =150 – 25 = 125
Assume that after 10 days, the remaining food is sufficient for 125 men for x days
More men, less days
Men {150:125}:: x:35
150 x 35 = 125x=> 6x35= 5x=>x = 6x7 = 42
The remaining food is sufficient for 125 men for 42 days
|
Question 49
|
14 pumps of equal capacity can fill a tank in 6 days. If the tank has to be filled in 4 days, the number of extra pumps need is?
|
A
|
7
|
|
B
|
21
|
|
C
|
14
|
|
D
|
28
|
Question 49 Explanation:
The total volume of the tank is constant. The volume of water which one pump supplies in one day is constant.
As more pumps are used the time to fill the tank will decrease
4:6:: 14: x
Or 4x = 6*14
Or x= 6*14/4 = 21
Extra pumps needed = (21-14) = 7
As more pumps are used the time to fill the tank will decrease
4:6:: 14: x
Or 4x = 6*14
Or x= 6*14/4 = 21
Extra pumps needed = (21-14) = 7
|
Question 50
|
In a dairy farm, 40 cows eat 40 bags of husk in 40 days. How many days one cow will eat one bag of husk?
|
A
|
1
|
|
B
|
40
|
|
C
|
26
|
|
D
|
20
|
Question 50 Explanation:
Assume that in x days, one cow will eat one bag of husk.
Less cows, more days
Less bags, less days
Hence, we can write as
[Cow 1:40 bags 40:1]
1 x 40 * x = 40*1 * 40
X= 40
Less cows, more days
Less bags, less days
Hence, we can write as
[Cow 1:40 bags 40:1]
1 x 40 * x = 40*1 * 40
X= 40
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