## Practice Problems on Pipes and Cistern

1. A Special pump can be used for filling as well as for emptying a Cistern. The capacity of the Cistern is 2400m³. The emptying capacity of the Cistern is 10m³ per minute higher than its filling capacity and the pump needs 8 minutes lesser to Cistern the tank than it needs to fill it. What is the filling capacity of the pump?
A. 40m³/min
B. 50m³/min
C. 60m³/min
D. 30m³/min
E. None of the Above
Explanation :
Filling Capacity of the Pump = x m/min
Emptying Capacity of the pump = (x+10) m/min
2400/x – 2400/x+10 = 8
(x – 50) + (x + 60) = 0
x = 50
2. Three pipes P, Q and R can fill a Cistern in 6 hours. After working at it together for 2 hours, R is closed and P and Q can fill the remaining part in 7 hours. The number of hours taken by R alone to fill the Cistern is
A. 14 hours
B. 12 hours
C. 15 hours
D. 18 hours
E. None of the Above
Explanation :
Part filled in 2 hours = 2/6 = 1/3
Remaining Part = (1-1/3) = 2/3
(P + Q)’s 7 hour work = 2/3
(P + Q)’s 1 hour work = 2/21
R’s 1 hour work = (P + Q + R) 1 hour work – (P + Q) 1 hour work
= (1/6 – 2/21) = 1/14 = 14 hours
3. A Cistern is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open,how long will it take to empty or fill the tank completely?
A. 5 minutes
B. 4 minutes
C. 6 minutes
D. 8 minutes
E. None of the Above
Explanation :
pipe B is faster than pipe A and so,the tank will be emptied.
part to be emptied = 2/5
part emptied by (A+B) in 1 minute= (1/6 – 1/10) = 1/15
1/15 : 2/5 :: 1: x
2/5 * 15 = 6 minutes.
4. If a pipe A can fill a tank 3 times faster than pipe B. If both the pipes can fill the tank in 32 minutes, then the slower pipe alone will be able to fill the tank in?
A. 128 minutes
B. 124 minutes
C. 154 minutes
D. 168 minutes
E. None of the Above
Explanation :
Time is taken by pipe A = x
Time is taken by pipe B = x/3
1/x + 3/x = 1/32
x = 128 minutes
5. A large cistern can be filled by two pipes P and Q in 15 minutes and 20 minutes respectively. How many minutes will it take to fill the Cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half?
A. 12 minutes
B. 17 minutes
C. 18 minutes
D. 19 minutes
E. None of the Above
Explanation :
Part filled by P and Q = 1/15 + 1/20 = 7/60
Part filled by Q = 1/20
x/2(7/60 + 1/20) = 12 minutes
6. A pipe can fill a cistern in 16 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the cistern completely?
A. 3 hours
B. 2 hours
C. 9 hours
D. 4 hours
E. None of the Above
Explanation :
In One hour pipe can fill = 1/16
Time is taken to fill half of the tank = 1/2 * 16 = 8 hours
Part filled by four pipes in one hour = (8*1/16) = 1/2
Required Remaining Part = 1/2
Total time = 8 + 1 = 9
7. Two pipes P and Q are opened together to fill a tank. Both the pipes fill the tank in time “x” If Q separately took 25 minutes more time than “x” to fill the tank and Q took 49 minutes more time than “x” to fill the tank, then find out the value of x?
A. 48 minutes
B. 35 minutes
C. 54 minutes
D. 68 minutes
E. None of the Above
Explanation :
Time is taken to fill the tank by both Pipes x = √a*b
x = √25*49 = 5 * 7 = 35
8. Three taps P, Q and R can fill a tank in 12, 15 and 20 hours respectively. If P is open all the time and Q, R are open for one hour each alternatively, the tank will be full in
A. 3 hours
B. 2 hours
C. 7 hours
D. 4 hours
E. None of the Above
Explanation :
(P + Q)’s 1 hour work = 1/12 + 1/15 = 3/20
(P + R)’s 1 hour work = 1/12 + 1/20 = 2/15
For 2 hrs = (3/20 + 2/15) = 17/60
For 6 hrs = (3*17/60) = 17/20
Remaining Part = 1 – 17/20 = 3/20 filled by P and Q in 1 hour
9. Pipe A fills a tank in 30 minutes. Pipe B can fill the same tank 5 times as fast as pipe A. If both the pipes were kept open when the tank is empty, how much time will it take for the tank to overflow?
A. 3 minutes
B. 2 minutes
C. 5 minutes
D. 4 minutes
E. None of the Above
Explanation :
Total Capacity = 90L.
Tank filled in 1 minute by A = 3L
Tank filled in 1 minute by B = 15L
The capacity of the tank filled with both A and B in 1 minute = 18L.
overflow = 90/18 = 5 minutes.
10. Two pipes P and Q can fill a cistern in 10 hours and 20 hours respectively. If they are opened simultaneously. Sometimes later, tap Q was closed, then it takes total 5 hours to fill up the whole tank. After how many hours Q was closed?
A. 14 hours
B. 15 hours
C. 10 hours
D. 16 hours
E. None of the Above
Explanation :
Pipe P Efficiency = 100/10 = 10%
Pipe Q Efficiency = 100/20 = 5%
Net Efficiency = 15%
15x + 10(5-x) = 100
x = 10
11. If a pipe A can fill a tank 3 times faster than pipe B and takes 32 minutes less than pipe B to fill the tank. If both the pipes are opened simultaneously, then find the time taken to fill the tank?
A. 14 minutes
B. 12 minutes
C. 15 minutes
D. 16 minutes
E. None of the Above
Explanation :
3x – x = 32
x = 16
1/16 + 1/48 = 4/48
Time taken to fill the tank = 48/4 = 12 minutes
12. Two pipes P and Q can fill a tank in 24 minutes and 27 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 8 minutes?
A. 14 minutes
B. 12 minutes
C. 15 minutes
D. 18 minutes
E. None of the Above
Explanation :
Required time = y(1-(t/x)) = 27(1-(8/24))= 18 minutes
13. A full tank gets emptied in 8 minutes due to the presence of a leak in it. On opening a tap which can fill the tank at the rate of 9 L/min, the tank get emptied in 12 min. Find the capacity of a tank?
A. 120 L
B. 240 L
C. 216 L
D. 224 L
E. None of the Above
Explanation :
a = 8; b = 9; C = 12
Capacity of a tank = a*b*c/c-a = 8*9*12/4 = 216 Litre.
14. If a pipe A can fill a tank 3 times faster than pipe B. If both the pipes can fill the tank in 42 minutes, then the slower pipe alone will be able to fill the tank in?
A. 148 minutes
B. 124 minutes
C. 154 minutes
D. 168 minutes
E. None of the Above
Explanation :
Time is taken by pipe A = x
Time is taken by pipe B = x/3
1/x + 3/x = 1/42
x = 168 minutes
15. A large cistern can be filled by two pipes P and Q in 15 minutes and 10 minutes respectively. How many minutes will it take to fill the Cistern from an empty state if Q is used for half the time and P and Q fill it together for the other half?
A. 6.5 minutes
B. 7.5 minutes
C. 8.5 minutes
D. 9.5 minutes
E. None of the Above
Explanation :
Part filled by P and Q = 1/15 + 1/10 = 1/6
Part filled by Q = 1/10
x/2(1/6 + 1/10) = 2/15 = 15/2 = 7.5 minutes
16. A pipe can fill a cistern in 8 hours. After half the tank is filled, three more similar taps are opened. What is the total time taken to fill the cistern completely?
A. 3 hours
B. 2 hours
C. 5 hours
D. 4 hours
E. None of the Above
Explanation :
In One hour pipe can fill = 1/8
Time is taken to fill half of the tank = 1/2 * 8 = 4 hours
Part filled by four pipes in one hour = (4*1/8) = 1/2
Required Remaining Part = 1/2
Total time = 4 + 1 = 5
17. Two pipes P and Q are opened together to fill a tank. Both the pipes fill the tank in time “x” If Q separately took 16 minutes more time than “x” to fill the tank and Q took 36 minutes more time than “x” to fill the tank, then find out the value of x?
A. 48 minutes
B. 24 minutes
C. 54 minutes
D. 68 minutes
E. None of the Above
Explanation :
Time is taken to fill the tank by both Pipes x = √a*b
x = √16*36 = 4 * 6 = 24
18. A Cistern has an inlet pipe and outlet pipe. The inlet pipe fills the cistern completely in 1 hour 20 minutes when the outlet pipe is plugged. The outlet pipe empties the tank completely in 6 hours when the inlet pipe is plugged. If there is a leakage also which is capable of draining out the water from the tank at half of the rate of the outlet pipe, then what is the time taken to fill the empty tank when both the pipes are opened?
A. 3 hours
B. 2 hours
C. 5 hours
D. 4 hours
E. None of the Above
Explanation :
Inlet pipe Efficiency = 100/(8/6) = 75%
Outlet pipe Efficiency = 100/(6) = 16.66%
Efficiency of leakage = half of the rate of the outlet pipe = 8.33%
Net Efficiency = 75 – (16.66 + 8.33) = 50%
Required time = 100/50 = 2 hours
19. A Cistern has an inlet pipe and outlet pipe. The inlet pipe fills the cistern completely in 1 hour 20 minutes when the outlet pipe is plugged. The outlet pipe empties the tank completely in 4 hours when the inlet pipe is plugged. If both pipes are opened simultaneously at a time when the tank was one-third filled, when will the tank fill thereafter?
A. 3 hours
B. 2 hours
C. 5 hours
D. 4 hours
E. None of the Above
Explanation :
Inlet pipe Efficiency = 100/(8/6) = 75%
Outlet pipe Efficiency = 100/(4) = 25%
Net Efficiency = 75 – 25 = 50%(1/3)filled
2/3 filled = 100%
Required time = 100/50 = 2 hours
20. Two pipes P and Q can fill a cistern in 10 hours and 20 hours respectively. If they are opened simultaneously. Sometimes later, tap Q was closed, then it takes total 8 hours to fill up the whole tank. After how many hours Q was closed?
A. 4 hours
B. 5 hours
C. 2 hours
D. 6 hours
E. None of the Above
Explanation :
Pipe P Efficiency = 100/10 = 10%
Pipe Q Efficiency = 100/20 = 5%
Net Efficiency = 15%
15x + 10(8-x) = 100
x = 4
21. Three pipes A, B, and C can fill the tank in 10 hours, 20 hours and 40 hours respectively. In the beginning all of them are opened simultaneously. After 2 hours, tap C is closed and A and B are kept running. After the 4th hour, tap B is also closed. The remaining work is done by tap A alone. What is the percentage of the work done by tap A alone?
A. 30 %
B. 35 %
C. 45 %
D. 50 %
E. None of the Above
Explanation :
Pipe A’s work in % = 100/10 = 10%
Pipe B’s work in % = 100/20 = 5%
Pipe C’s work in % = 100/40 = 2.5%
All of them are opened for 2 hours + after 2 hours, tap C is closed + After the 4th hour, tap B is also closed = 100
=> (10+5+2.5)*2 + (10+5)*2 + X = 100
=> 35 + 30 + work by tap A alone = 100
=> work by tap A alone = 100-65 = 35%
22. A pipe can fill a tank in 12 minutes and another pipe can fill it in 15 minutes, but a third pipe can empty it in 6 minutes. The first two pipes are kept open for 5 min in the beginning and then third pipe is also opened. Time taken to empty the water tank is?
A. 30 mins
B. 25 mins
C. 45 mins
D. 50 mins
E. None of the Above
Explanation :
x/6 – (x+5)/12 – (x+5)/15 = 0
x = 45 mins
23. Two pipes A and B can fill a tank in 12 hours and 18 hours respectively. The pipes are opened simultaneously and it is found that due to leakage in the bottom of the tank it took 48 minutes excess time to fill the cistern. When the cistern is full, in what time will the leak empty it?
A. 72 hours
B. 62 hours
C. 64 hours
D. 84 hours
E. None of the Above
Explanation :
Work done by the two pipes in 1 hour = (1/12)+(1/18) = (15/108).
Time taken by these pipes to fill the tank = (108/15)hrs = 7 hours 12 min.
Due to leakage, time taken = 7 hours 12 min + 48 min = 8 hours
Work done by two pipes and leak in 1 hour = 1/8.
Work done by the leak in 1 hour =(15/108)-(1/8)=(1/72).
Leak will empty the full cistern in 72 hours.
24. A tank is normally filled in 6 hours but takes two hours longer to fill because of a leak in the bottom of the tank. If the tank is full the leak will empty it in how many hours?
A. 16 hours
B. 18 hours
C. 17 hours
D. 24 hours
E. None of the Above
Explanation :
Work done by leak in 1 hr=(1/6-1/8)=1/24
Leak will empty the tank in 24 hours
25. Twelve pipes are connected to a Cistern. Some of them are inlet pipes and the others are outlet pipes. Each of the inlet pipes can fill the tank in 8 hours and each of the outlet pipes can empty the cistern completely in 6 hours. If all the pipes are kept open, the empty tank gets filled in 24 hours. How many inlet pipes are there?
A. 6
B. 8
C. 7
D. 4
E. None of the Above
Explanation :
(x/8)-[(12-x)/6] = 1/24
x = 7
26. A dam has four inlets – A, B, C and D. The dam can be filled in 12 minutes through the first three inlets and it can be filled in 15 minutes through the second, the third and fourth inlet also it can be filled through the first and the fourth inlet in 20 minutes. How much time required to fill up the dam by all the four inlets?
A. 10 mins
B. 15 mins
C. 20 mins
D. 25 mins
E. None of the Above
Explanation :
(1/A + 1/B + 1/C) = 1/12 …(i)
(1/B + 1/C + 1/D) = 1/15 …(ii)
(1/A + 1/D) = 1/20 …(iii)
From eqn (i) and (ii)
(1/A – 1/D) = 1/60…(iv)
From eqn (iii) and (iv)
A=30 D=60.
Let the time taken to full the tank = T
T(1/A + 1/B +1/C +1/D)= 1
T(1/30 + 1/15) = 1
T = 10 mins
27. Three pipes P, Q and R connected to a Cistern. The first pipe (i.e) P can fill 1/2 part of the tank in one hour, second pipe, Q can fill 1/3 part of the cistern in one hour. R is connected to empty the cistern. After opening all the three pipes 7/12 part of the cistern. Then how much time required to empty the cistern completely?
A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. None of the Above
Explanation :
In 1 hour, P can fill = 1/2 Part
Time taken to fill the Cistern by Pipe P = 2 hours
In 1 hour, Q can fill = 1/3 Part
Time taken to fill the Cistern by Pipe P = 3 hours
[1/2 + 1/3 – 1/R] = 7/12
1/R = 1/4
Time required to empty the Cistern = 4 hours
28. A Cistern can be filled by an inlet pipe at the rate of 4 litres per minute. A leak in the bottom of a cistern can empty the full tank in 8 hours. When the cistern is full, the inlet is opened and due to the leak, the cistern is empty in 40 hours. How many litres does the cistern hold?
A. 4000 litre
B. 2400 litre
C. 1920 litre
D. 2020 litre
E. None of the Above
Explanation :
Part emptied by the leak in 1 hour = 1/8
part filled by (leak & inlet open) in 1 hour = 1/40
Part filled by the inlet pipe in 1 hour = 1/8 – 1/40 = 1/10
Inlet pipe fills the tank in = 10 hours
Inlet pipe fills water at the rate of 4 litres a minute.
Capacity of Cistern = 10 * 60 * 4 = 2400 litre
29. In a tank there is a pipe which can be used for filling the tank as well as for emptying it. The capacity of the tank is 1200 m³. The emptying of the tank is 10 m³ per minute higher than its filling capacity and the pump needs 6 minutes lesser to empty the tank than it needs to fill it. What is the filling capacity of the pipe?
A. 20 m³ / min.
B. 40 m³ / min.
C. 50 m³ / min.
D. 60 m³ / min.
E. None of the Above
Answer – B. 40 m³ / min.
Explanation :
1200/x – 1200/(x+10) = 6
200/x – 200/(x+10) = 6
x2 + 10x – 2000 = 0
x = 40
30. Two pipes P and Q can fill a cistern in 12 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, in how many hours will the tank be full?
A. 4 hours
B. 5 hours
C. 2 hours
D. 6 hours
E. None of the Above
Explanation :
Pipe P can fill = 1/12
Pipe Q can fill = 1/4
For every two hour, 1/12 + 1/4 = 1/3 Part filled
Total = 6 hours
31. Two pipes A and B can fill a tank in 10 hours and 15 hours respectively while a third pipe C can empty the full tank in 20 hours. All the pipes are opened for 5 hours and then C is closed. Find the time in which the tank is full?
a) 5.5 hrs
b) 6.5 hrs
c) 7.5 hrs
d) 8.5 hrs
e) None of these
Explanation :
(1/10 + 1/15 – 1/20)*5 + (1/10 + 1/15)*T = 1. We will get T = 2.5 hrs
so total time = 5 + 2.5 = 7.5 hrs
32. Three pipe P, Q and R can fill a tank in 12 minutes, 18 minutes and 24 minutes respectively. The pipe R is closed 12 minutes before the tank is filled. In what time the tank is full?
a) 8.(5/13) hrs
b) 8.(4/13) hrs
c) 7.(4/13) hrs
d) 8.(6/13) hrs
e) None of these
Explanation :
Let T is the time taken by the pipes to fill the tank
(1/12 + 1/18 + 1/24)*(T – 12) + (1/12 + 1/18)*12 = 1
We will get T = 108/13 = 8.(4/13) hrs
33. On pipe P is 4 times faster than pipe Q and takes 45 minutes less than pipe Q. In what time the cistern is full if both the pipes are opened together?
a) 8 minutes
b) 10 minutes
c) 12 minutes
d) 14 minutes
e) None of these
Explanation :
Let P takes x minutes to fill the tank alone, then Q will take 4x minutes to fill the tank
4x – x = 45, x = 15
So P will take 15 minutes and Q will take 60 minutes to fill the tank. Both will fill the tank in
(60*15)/(75) = 12 minutes
34. Two pipes can fill a tank in 15 and 20 hours respectively. The pipes are opened simultaneously and it is found that due to the leakage in the bottom, 17/7 hours extra are taken extra to fill the tank. If the tank is full, in what approximate time would the leak empty it?
a) 27 hrs
b) 32 hrs
c) 36 hrs
d) 39 hrs
e) None of these
Explanation :
Total time taken by both pipes before the leak was developed = 60/7 hours
now, leaks is developed which will take T time to empty the tank so, (1/15 +1/20 – 1/T) = 1/11
solve for T, we will get 660/17 hours = 39 hours (approx.)
35. Two pipes A and B can fill a tank in 8 minutes and 12 minutes respectively. If both the pipes are openedsimultaneously, after what time should B be closed so that the tank is full in 6 minutes?
a) 1 min
b) 2 min
c) 3 min
d) 4 min
e) None of these
Explanation :
Let after x minutes pipe B is closed
(1/8 + 1/12)*x + (1/8)*(6 -x) = 1
X= 3 minutes
36. In what time would a cistern be filled by three pipes whose diameters are 1cm, 2 cm and 3 cm running together, when the largest pipe alone can fill the tank in 21 minutes? The amount of water flowing through the pipe is directly proportional to the square of its diameter.
a)10.5 minutes
b) 11.5 minutes
c) 12.5 minutes
d) 13.5 minutes
e) None of these
Explanation :
More the diameter more will be the water flowing through it and less will be the time taken.
Means bigger pipe will take less time to fill the tank
So, for 1 cm time, (1^2)/(3^2) = 21/t, we get t = 189
For 2 cm time, (2^2)/(3^2) = 21/t. We get t = 189/4
So total time = 1/21 + 1/189 + 4/189 = 2/27
So total time = 13.5 minutes
37. Two pipes P and Q can fill a tank in 10 min and 12 min respectively and a waste pipe can carry off 12 litres of water per minute. If all the pipes are opened when the tank is full and it takes one hour to empty the tank. Find the capacity of the tank.
a) 30
b) 45
c) 60
d) 75
e) None of these
Explanation :
Let the waste pipe take ‘T’ time to empty the tank.
(1/10 + 1/12 – 1/T)*60 = -1
We will get T = 5 min
So capacity = 5*12 = 60ltr
38. One pipe fill 1/4 of the tank in 4 minutes and another pipe fills 1/5 of the tank in 4 minutes. Find the time taken by both pipe together to fill half the tank?
a) 40/9 minutes
b) 50/9 minutes
c) 44/9 minutes
d) 53/9 minutes
e) None of these
Explanation :
First pipe will take 16 minutes to fill the tank alone. Similarly second pipe will take 20 minutes to fill the tank alone. Let T is the time in which both the pipes will fill half the tank
(1/16 + 1/20)*T = 1/2, we get T = 40/9 minutes
39. Two pipes can separately fill the tank in 15hrs and 30hrs respectively. Both the pipe are opened and when the tank is 1/3 full a leak is developed due to which 1/3 water supplied by the pipe leaks out. What is the total time to fill the tank?
a) 20/3 hr
b) 35/3 hr
c) 40/3 hr
d) 50/3 hr
e) None of these
Explanation :
(1/15 + 1/30)*T1 = 1/3, T1 = 10/3 hr
Now after leak is developed, [(1/15 + 1/30) – (1/3)*(1/15 + 1/30)]*T2 = 2/3
T2 = 10 hr. So total time = 10 + 10/3 = 40/3 hr
40. Three pipes A, B and C is attached to a cistern. A can fill it in 20 minutes and B can fill it in 30 minutes. C is a waste pipe.  After opening both the pipes A and B, Riya leaves the cistern to fill and returns when the cistern is supposed to be filled. But she found that waste pipe C had been left open, she closes it and now the cistern takes 5 minutes more to fill. In how much time the pipe C can empty the full cistern?
a) 26.8 minutes
b) 25.8 minutes
c) 27.8 minutes
d) 28.8 minutes
e) None of these