Explanation / Important formulas:
Inlet: A pipe connected with a tank or a cistern or a reservoir that fills it, is known as an inlet.
Outlet: A pipe connected with a tank or cistern or reservoir emptying it, is known as an outlet.
- If a pipe can fill a tank in x hours, then:part filled in 1 hour = 1 / x
- If a pipe can empty a tank in y hours, then:part emptied in 1 hour = 1
- If a pipe can fill a tank in y/x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then the net part filled in 1 hour = (1/x – 1/y)
- If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where x > y), then on opening both the pipes, then the net part emptied in 1 hour = (1/y – 1/x)
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Pipes and Cisterns - Test
Pipes and cisterns - Question and Answers
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Question 1
|
12minutes
|
|
13.5 minutes
|
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15minutes
|
|
14.5 minutes
|
1/60th of the tank is emptied by pipe C in 1 minutes
Part of tank filled in the first 6 minutes = 6*[(1/20)+(1/30)] = ½
When all pipes are opened, part of tank filled in 1 minutes = (1/12)-(1/60) = 1/15
Time required to fill the remaining ½ of the tank = (1/2) / (1/15) = 7.5
Total time = 6+7.5 = 13.5 minutes
Question 2
|
12
|
|
15
|
|
20
|
|
18
|
= (1/20) + (1/10) – (1/15) = 1/12
Time taken to fill the tank = 12 minutes
Question 3
|
7 liters
|
|
5 liters
|
|
3.5 liters
|
|
2.5 liters
|
Part of tank emptied by Q in an hour = 1/1.5 = 2/3
Part of tank filled by R in an hour = ½
Part of tank filled by S in an hour = 1/ 2.5 = 2/5
Part of tank emptied in an hour = (1+ (2/3)) - (1/2 + (2/5)) = 23/30
Water remaining in the tank = 15*7/30 = 3.5 liters
Question 4
|
180 minutes
|
|
167 minutes
|
|
200 minutes
|
|
178 minutes
|
Part filled in 165 minutes = (165/3) * (1/60) = 55/60
Part filled in 167 minutes = (55/60) + (1/20) + (1/30) = 60/60 = 1
The tank is filled in 167 minutes
Question 5
|
30 minutes
|
|
45 minutes
|
|
40 minutes
|
|
25 minutes
|
Part of tank filled by B in a minutes =1/75
Let pipe B be closed after x minutes
Part of tank filled in x minutes= x*[(1/60)+(1/75)]
= 9x / 300
Part of tank filled in (40-x) minutes = [(40-x)*(1/60)]
= (40-x) / 60
(9x / 300) + ((40 - x) / 60) = 1
4x = 100
X= 25
Question 6
|
60 minutes
|
|
40 minutes
|
|
30 minutes
|
|
20 minutes
|
Part of the tank filled by A and B = (1/60) + (1/x) = (1/20)
Solving this, x= 30
Question 7
|
10 minutes
|
|
7/6 hours
|
|
6/7 hours
|
|
7hours
|
1hr 10 min = 1+(1/6) = 7/6 hrs
1- (1/x) = 1/ (7/6) = 6/7
Part of tank leaked in an hour = 1-6/7 = 1/7
The leak takes7 hours to drain all the water
Question 8
|
6 minutes
|
|
12 minutes
|
|
12.5 minutes
|
|
24 minutes
|
Part of the tub filled in the next 2 minutes = 2*1/15 = 2/15
Part of the filled in 4 minutes = (1/5) +(2/15) =1/3
Time required to fill the tub = 3*4 = 12 minutes
Question 9
|
7 minutes
|
|
14 minutes
|
|
3.5 minutes
|
|
28 minutes
|
(7/2x) = ¼
x=14
x /2 = 7
Question 10
|
480 liters
|
|
360 liters
|
|
300 litres
|
|
240 liters
|
Part of the tank emptied by the outlet in a minute = 1 / (5*60) = 1/300
Part of the tank filled in the first 30 minutes = 30*[(1/x) - (1/300)]
= (300 - x) / 10x
Part of the tank filled in the next 36minutes = 36 * (1/x)
1 – [(300 - x) / 10 x] = 36 / x
Solving, x= 60
Capacity of tank = 60 * 5 = 300 liters
Question 11
|
10hours
|
|
5 hours
|
|
9 hours
|
|
6 hours
|
5x= 1+2+3+ .......+x
5x = x(x+1) / 2
X= 9 hours
Question 12
|
15 minutes
|
|
30 minutes
|
|
12 minutes
|
|
10 minutes
|
Part of tank filled by B in 1 minute = (1/20) / 3 = 1/60
Part of tank filled by them together in 1 min = (1/20) + (1/60) = 1/15
They take 15 min to fill the tank
Question 13
|
20 minutes
|
|
1 hour
|
|
30 minutes
|
|
60 minutes
|
Part of bucket filled by the tap in 1 minute =1/10
(1/10) – (1/x) = (1/12)
X = 60 minutes
Question 14
|
28
|
|
20
|
|
15
|
|
24
|
No. of buckets needed = 288 / 12 = 24
Question 15
|
100 minutes
|
|
75 minutes
|
|
90 minutes
|
|
80 minutes
|
Pipe A is closed before 30 minutes of overflow
Only pipe B was opened
Part of tank filled by pipe B in 30 minutes = ¼
The remaining 3/4th of the tank was filled by pipes A and B
To fill 3/4th of the tank together, 1 hour is taken
Time for overflow = 1 hours + 30 minutes
= 90 minutes
Question 16
|
3 hours
|
|
30 hours
|
|
10 hours
|
|
33 hours
|
= (1/6) +(1/10) + (1/15)
= 10/30
= 1/3
They take 3 hours
Question 17
|
4
|
|
5
|
|
6
|
|
7
|
Part of tank filled by an inlet pipe in an hour = 1/6
Part of tank drained by an outlet pipe in an hour =1/8
If all the pipes are opened, the tank is drained in half a day (12 hours)
Part of tank drained in an hour when all are open = 1/12
Part of tank drained by (10-x) outlet pipes – Part of tank filled by x inlet pipes = 1/12
[(10-x) / 8] – [x/6] = 1/12
Solving,
3(10-x)-4x = 2
30 – 7x = 2
7x=28
X=4
There are 4 inlet pipes and 6 outlet pipes
Question 18
|
70 cans
|
|
14 cans
|
|
28 cans
|
|
84 cans
|
1 can is filled in 2 minutes
14 cans can be filled in 28 minutes
Question 19
|
12 hours
|
|
18 hours
|
|
1day
|
|
2 days
|
Part of tank emptied by the leak in an hour = 1/x
Part of tank filled in an hour = (1/8) + (1/12) – (1-x)
=(5/24) – 1/x = 1/6
1/x = (5/24) –(1/6)
= 1/24
X= 24 hours
Question 20
|
2 hours
|
|
4 hours
|
|
4.5 hours
|
|
3 hours
|
Part of tank filled by pipe A in an hour = ¼
In the first hour, 1/4th of the tank is filled.
The remaining 3/4th of the tank is filled by A and B together
Part of tank filled by A and B in an hour = (1/4) +(1/8) = 3/8
Time taken to fill ¾ of the tank = (3/4) / (3/8) = 2 hours
The cistern is filled in 1+ 2 = 3 hours
Question 21
|
4.5 hours
|
|
6 hours
|
|
7.5 hours
|
|
) 7.5 hours
|
(1/y) = (1/3) – (1/5)
= 2/ 15
Y takes 15/2 = 7.5 hours to fill the tank
Question 22
|
360 liters
|
|
216 liters
|
|
180 liters
|
|
144 liters
|
= 180 * 1.2
= 216 liters
Question 23
|
1 hr 40 min
|
|
36 mins
|
|
20 mins
|
|
24 mins
|
=5/120
= 1/24
It takes 24 minutes to fill the tank
Question 24
|
12 hours
|
|
145 hours
|
|
18 hours
|
|
24 hours
|
Question 25
|
1 hour
|
|
36 min
|
|
45 min
|
|
54 min
|
Part of tank filled by pipe B in 1 minute = 1/90
Part of tank emptied by the outlet in 1 minute = 1/60
Part of tank filled when all the pipes are opened = part of tank filled by inlet-part of tank emptied by outlet = (1/30) + (1/90) – (1/60)
= (6+2-3) / 180
= 1/ 36
The tank is filled in 36 mins
Question 26
|
70mins
|
|
(7/5)hrs
|
|
21(3/7)mins
|
|
42 mins
|
Full cistern is emptied in 30*7/5 = 42 minutes
Question 27
|
35 mins
|
|
30 mins
|
|
25 mins
|
|
20 mins
|
Part of cistern filled by A in 15 mins = 15/60 = ¼
Part of cistern filled by A and B in 1 minute = (1/60)+(1/30) = 1/20
¾ th of the cistern is filled by A and B
Time taken to fill ¾ of the cistern = (3/4) /(1/20) = 15 minutes
The cistern is filled in 30 minutes
Question 28
|
40 mins
|
|
1 hour
|
|
75 mins
|
|
90 mins
|
Part of tank filled by taps A in 1 minute = 1/120
(1/A) + (1/B) = (1/30)
(1/B) = (1/30) –(1/120) = (1/40)
B alone takes 40 mins to fill the tank
Question 29
|
22 minutes
|
|
15 minutes
|
|
11 minutes
|
|
6 minutes
|
Part of tank filled in the first 2 minutes = 2*1/6 = 1/3
2/3 of the tank is filled by X alone
Time taken by X to fill 2/3 of the tank = (2/3) / (1/33)
= 22 minutes
Question 30
|
20 hours
|
|
18 hours
|
|
24 hours
|
|
22.5 hours
|
Part of tank filled by B in 1 hour = 1/45
Part of tank filled by both in 1 hour = (1/36) + (1/45)
= 81 / (36*45)
= 1/20
They can fill the tank in 20 hours
Question 31
|
18
|
|
10
|
|
15
|
|
8
|
Question 32
|
18 hrs
|
|
36 hrs
|
|
35 hrs
|
|
9 hrs
|
They take 4 hours to fill the tank. But due to the leak, they take 4.5 hours to fill the tank
Part of tank emptied by leak in 1 hours = ¼ - 1/ 4.5
= ¼ - 2/9
= 1/36
The leak can empty the tank in 36 hours
Question 33
|
192 mins
|
|
144 mins
|
|
108 mins
|
|
81 mins
|
1/x + 1/3x = 1/36
4/3x = 1/36
X= 48
3x = 144
Question 34
|
30/17
|
|
30/11
|
|
9/2
|
|
60/17
|
= 17/60
The tank will be filled in (60/17 ) hours
Question 35
|
4 hrs
|
|
3hrs 45 mins
|
|
4 hrs 15 mins
|
|
3 hrs 15 mins
|
Now, 4 taps are filling the tank
Time taken by 1 tap to fill half the tank = 3
Time taken by 4 taps to fill half the tank = ¾
Total time taken = 3 hrs 45mins
Question 36
|
6.5 hrs
|
|
4.5 hrs
|
|
5 hrs
|
|
7.2 hrs
|
The cistern gets filled in 36/5 = 7.2 hours
Question 37
|
10 hrs
|
|
15 hrs
|
|
30 hrs
|
|
6 hrs
|
B = A -5
B = C + 4
C =A – 9
1/A + 1/(A-5) = 1/(A-9)
1/(A - 9) – 1/(A-5) = 1/A
Substitute the options given in the place of A
If A = 10,
1 – 1/5 not equal to 1/10
If A = 15,
1/6 – 1/10 = 1/15
So, A = 15
Question 38
|
1/11
|
|
5/11
|
|
6/11
|
|
8/11
|
= 3 * [(1/30)+(1/20)+(1/10)]
= 11/20
Part of tank filled by C in 3 minutes
= 3/10
Ratio = 3/10 : 11/20
= 6: 11
Question 39
|
17 minutes
|
|
12 minutes
|
|
19 minutes
|
|
21 minutes
|
1/x = 1/30 = 1/40 = 7/120
X= 120/7 = 17. 14 minutes
Question 40
|
16 mins
|
|
32 mins
|
|
48 mins
|
|
40 mins
|
1/x = 1/P – 1/Q
= 1/16 – 1/32
= 1/32
X= 32 mins
Question 41
|
8 hrs
|
|
6 hrs
|
|
2 hrs
|
|
1 hrs
|
B= A+6
We can check the options to find the answer
If A=8,
1/8 + 1/1 4 not equal to ¼
If A = 6,
1/6 + 1/12 = ¼
So, A = 6
Question 42
|
3.5
|
|
2
|
|
3
|
|
2.5
|
= (1/A) + (1/B) + (1/C)
=(1/5) + (1/10) + (1/30)
= 1/3
The tank will be filled in 3 hours
Question 43
|
8 hrs
|
|
14 hrs
|
|
7 hrs
|
|
13/3
|
½ - 1/x = 3/7
1/x = ½ - 3/7 = 1/14
X= 14
Question 44
|
6mins to fill
|
|
9 mins to fill
|
|
6 mins to empty
|
|
9 mins to empty
|
Part of tank emptied by B in 1 minute = 1/6
The rate at which pipe B empties is higher than the rate at which the pipe A fills the tank
Part of tank emptied in 1minute when A and B are opened = 1/6 – 1/10
= 1/ 15
Time taken to empty 2/5th of the tank
= 2/5 / 1/15
= 6 minutes
Question 45
|
10 mins
|
|
15 mins
|
|
12 mins
|
|
20 mins
|
= 1/15
Part of tank filled by both the taps in 10 minutes = 2/3
The remaining 1/3 of the tank is filled by the second tap alone.
Time taken to fill 1/3 of the tank = (1/3) /(1/60)
= 20 minutes
Question 46
|
8
|
|
15
|
|
16
|
|
18
|
= 162 litres
Number of 9 liters buckets needed = (162/9) = 18
Question 47
|
60 hrs
|
|
80 hrs
|
|
70 hrs
|
|
90 hrs
|
The leak will empty the cistern in 90 hrs
Question 48
|
5mins
|
|
12 mins
|
|
10 mins
|
|
15(2/3) mins
|
= 1/20 + 1/15 + 1/12
= 1/5
The cistern will be filled in 5 mins
Question 49
|
7mins 45 sec
|
|
8 mins 5 sec
|
|
7 mins 15 sec
|
|
8 mins 15 sec
|
= (1/A) + (1/B)
= 3/20
Part of the bucket filled by A and B in 3 minutes = 9/20
The remaining 11/20 of the bucket is filled by B alone
Time taken = (11/20) / (1/15)
= 33/4 minutes
= 8 mins 15 seconds
Question 50
|
7 hrs
|
|
7hrs 30 mins
|
|
8 hrs
|
|
8 hrs 30 mins
|
= 2/15
The tank will be filled in 15/2 hrs
= 7 hrs 30 minutes
Question 51
|
5 hrs
|
|
12.5 hrs
|
|
6 hrs
|
|
7.5 hrs
|
= 1/6
The tank will be filled in 6 hours
Question 52
|
5 hrs
|
|
7 hrs
|
|
6 hrs
|
|
8 hrs
|
Part of the cistern filled by the second tap in 1 hour = 1/3
Part of the cistern filled in 1 hour when both the taps are opened = (1/2) – (1/3)
= 1/6
The cistern will be filled in 6 hours
Question 53
|
8 minutes
|
|
12 minutes
|
|
10 minutes
|
|
16 minutes
|
= 1/10
The waste pipe takes 10 minutes to empty the cistern
Question 54
|
10 hrs 30 mins
|
|
21 hours
|
|
12 hours
|
|
24 hours
|
= 3.5 hours
= 7/2 hours
Work done by the leak in 1 hour
= (1/3) – (2/7)
= 1/21
The leak will empty the tank in 21 hours
Question 55
|
20 hrs
|
|
20 hrs
|
|
35 hrs
|
|
cannot be determined
|
Let the time taken by A to fill the tank be X hours
B is twice as fast as A
Time taken by B = x/2 minutes
C is twice as fast as B
Time taken by C = x/4 minutes
1/x + 2/x + 4/x = 1/5
X= 35
Question 56
|
10 mins 20sec
|
|
11mins 45 sec
|
|
12mins 30
|
|
15 mins
|
Part of tank filled by B in x minutes = x/40
Part of tank filled by A and B in 1 minute = 1/60 + 1/40
= 1/24
Part of tank filled by A and B in x minutes= x/24
x/40 + x/24 = 1
8x = 120
X = 15
The total time taken is 2x = 30 minutes
Question 57
|
15 mins
|
|
20 mins
|
|
27.5 mins
|
|
30 mins
|
Part of tank filled by B in x minutes = x/40
Part of tank filled by A and B in x minutes = x/40 + x/60
x/40 + x/40 +x/60 =1
x= 15
2x = 30
Question 58
|
10
|
|
12
|
|
14
|
|
16
|
The remaining 2/3 of the tank is filled by A and B in 7 hours
Part of tank filled by A and B in 1 hour = (2/3) / 7 = 2/21
1/C = 1/6 – 2/21
= 3/42
= 1/14
C alone can fill the tank in 14 hours
Question 59
|
4hrs 30 mins
|
|
5hrs
|
|
5 hrs 15 mins
|
|
5 hrs 30 mins
|
1/4th of the tank is filled by 3 pipes in ½ hours
Time taken by the pipe to fill ¾ of the tank = 6*3/4 = 9/2
Total time taken = ½ + 9/2 = 5 hours
Question 60
|
72 mins
|
|
80 mins
|
|
100 mins
|
|
90 mins
|
1/D = 1/36 – 1/60 = 1/90
D alone takes 90 minutes to fill the tank
Question 61
|
15
|
|
12
|
|
14
|
|
41
|
Remaining part = 1-1/3 = 2/3
(A+B)’s 1 hour work = 2/21
C’s 1 hour work = [(A+B+C)’s 1 hour work – (A+B)’s1 hour work]
= (1/6 – 2/21) = 1/14
C alone can fill the tank in 14 hours
Question 62
|
60 gallons
|
|
100 gallons
|
|
120 gallons
|
|
180 gallons
|
Volume of 1/40 part = 3 gallons
Volume of whole = 3 * 40 = 120 gallons
Question 63
|
3 ¼ min
|
|
5 ¼ min
|
|
8 ¼ min
|
|
9 ¼ min
|
X= 8 ¼
Question 64
|
5260 liters
|
|
5760 liters
|
|
5846 liters
|
|
6970 liters
|
X= 24 hrs
24 * 60 * 4 =5760
Question 65
|
4PM
|
|
5.30 PM
|
|
6PM
|
|
5 PM
|
2 to 3 = ¼ + 1/5 = 9/20
After 3AM = ¼ + 1/5 – ½ = - 1/20
¼ + 9/20 = 14/20
1 hr -----1/20
? --------14/20
14 hours 5 PM
Question 66
|
5/11
|
|
6/11
|
|
7/11
|
|
8/11
|
Question 67
|
1 13/17 hours
|
|
2 8/11
|
|
3 9/17
|
|
4 1/2 1
|
5 6 12 60
The tank will be full in 60 hours i.e., 3 9 hours.
17 17
Question 68
|
4 1/3 Hours
|
|
7 hours
|
|
8 hours
|
|
14 hours
|
2 7 14
Leak will empty the tank in 14 hrs.
Question 69
|
5 min.
|
|
9 min.
|
|
10 min.
|
|
15 min.
|
Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1.
x 2 + 1 + (30 - x). 2 = 1
75 45 75
11x + (60 -2x) = 1
225 75
11x + 180 - 6x = 225.
x = 9.
Question 70
|
6 hours
|
|
10 hours
|
|
15 hours
|
|
30 hours
|
Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank.
1 + 1 = 1
x (x - 5) (x - 9)
x - 5 + x = 1
x(x - 5) (x - 9)
(2x - 5)(x - 9) = x(x - 5)
x2 - 18x + 45 = 0
(x - 15)(x - 3) = 0
x = 15. [neglecting x = 3]
Question 71
|
81 min.
|
|
108 min.
|
|
144 min.
|
|
192 min.
|
Then, faster pipe will fill it in x minutes.
3
1 + 3 = 1
x x 36
4 = 1
x 36
x = 144 min.
Question 72
|
15 min
|
|
20 min
|
|
27.5 min
|
|
30 min
|
60 40 24
Suppose the tank is filled in x minutes.
Then, x 1 + 1 = 1
2 24 40
x x 1 = 1
2 15
x = 30 min.
Question 73
|
3 hrs 15 min
|
|
3 hrs 45 min
|
|
4 hrs
|
|
4 hrs 15 min
|
Part filled by the four taps in 1 hour = 4 x 1 = 2 .
6 3
Remaining part = 1 - 1 = 1 .
2 2
2 : 1 :: 1 : x
3 2
x = 1 x 1 x 3 = 3 hours i.e., 45 mins.
2 2 4
So, total time taken = 3 hrs. 45 mins.
Question 74
|
6 hours
|
|
6 2/3 hours
|
|
7 hours
|
|
7 1/2 houurs
|
d) 7 1 hours
2
Answer: Option C
Explanation:
(A + B)'s 1 hour's work = 1 + 1 = 9 = 3 .
12 15 60 20
(A + C)'s hour's work = 1 + 1 = 8 = 2 .
12 20 60 15
Part filled in 2 hrs = 3 + 2 = 17 .
20 15 60
Part filled in 6 hrs = 3 x 17 = 17 .
60 20
Remaining part = 1 - 17 = 3 .
20 20
Now, it is the turn of A and B and 3 part is filled by A and B in 1 hour.
20
Total time taken to fill the tank = (6 + 1) hrs = 7 hrs.
Question 75
|
10
|
|
12
|
|
14
|
|
16
|
6 3
Remaining part = 1 - 1 = 2 .
3 3
(A + B)'s 7 hour's work = 2
3
(A + B)'s 1 hour's work = 2
21
C's 1 hour's work = { (A + B + C)'s 1 hour's work } - { (A + B)'s 1 hour's work }
= 1 - 2 = 1
6 21 14
C alone can fill the tank in 14 hours.
Question 76
|
60 gallons
|
|
100 gallons
|
|
120 gallons
|
|
180 gallons
|
15 20 24
= 1 - 11
15 120
= - 1 . [-ve sign means emptying]
40
Volume of 1 part = 3 gallons.
40
Volume of whole = (3 x 40) gallons = 120 gallons.
Question 77
|
20 hours
|
|
25 hours
|
|
35 hours
|
|
Cannot be determined
|
|
None of these
|
Then, pipes B and C will take x and x hours respectively to fill the tank.
2 4
1 + 2 + 4 = 1
x x x 5
7 = 1
x 5
x = 35 hrs.
Question 78
|
1 hour
|
|
2 hours
|
|
6 hours
|
|
8 hours
|
Then, pipe B will fill it in (x + 6) hours.
1 + 1 = 1
x (x + 6) 4
x + 6 + x = 1
x(x + 6) 4
x2 - 2x - 24 = 0
(x -6)(x + 4) = 0
x = 6. [neglecting the negative value of x]
Question 79
|
12 min
|
|
15 min
|
|
15 min
|
|
50 min
|
20
Part filled by B in 1 min = 1 .
30
Part filled by (A + B) in 1 min = 1 + 1 = 1 .
20 30 12
Both pipes can fill the tank in 12 minutes.
Question 80
|
10 min. 20 sec
|
|
11 min. 45 sec.
|
|
12 min. 30 sec.
|
|
14 min. 40 sec.
|
15 20 15
Remaining part = 1 - 7 = 8 .
15 15
Part filled by B in 1 minute = 1
20
1 : 8 :: 1 : x
20 15
x = 8 x 1 x 20 = 10 2 min = 10 min. 40 sec.
15 3
The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec.