This Article consist of most important ” Pipes and Cistern Problems ” topic that are mostly asked in all competitive exams. We collected these questions from the students who appeared in exams. Now try to solve these questions.

## Pipes and Cistern Problems

**Question : 1** A cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 9 hours. If both the taps are opened simultaneously, then after how much time will the cistern get filled?

A. 4.5 hrs

B. 5 hrs

C. 6.5 hrs

D. 7.2 hrs

**Show Answer**

**Correct Answer : ** **D**

**Explanation : **

Net part filled in 1 hours = (1/4 -1/9)= 5/36.

The cistern will be filled in 36/5 hrs i.e., 7.2 hrs

**Question : 2 ** Two Pipes A and B can fill a tank in 6 hours and 4 hours respectively.If they are opened on alternate hours and if pipe A is opened first,in how many hours, the tank shall be full?

A. 4

B. 4.5

C. 5

D. 5.5

**Show Answer**

**Correct Answer : ** **C**

**Explanation : **

A’s work in 1 hour=1/6 , B’s work in 1 hour=1/4

(A + B)’s 2 hour’s work when opened alternatively=(1/6+1/4)=5/12.

(A + B)’s 2 hour’s work when opened alternatively=10/12=5/6

Now,it is A’s turn and 1/6 part is filled by A in 1 hour.

So, total time taken to fill the tank=(4+1) hrs=5 hrs

**Question : 3 ** Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is:

A. 60 gallons

B. 100 gallons

C. 120 gallons

D. 180 gallons

**Show Answer**

**Correct Answer : ** **C**

**Explanation : **

Work done by the waste pipe in 1 minute

= 1/15 – (1/20 + 1/24)

= (1/15 – 11/120)

= -1/40. [-ve sign means emptying]

Volume of 1/40 part = 3 gallons.

Volume of whole = (3 x 40) gallons = 120 gallons.

**Question : 4 ** Two pipes A and B can fill a cistern in (75/2) minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:

A. 5 min

B. 9 min

C. 10 min

D. 15 min

**Show Answer**

**Correct Answer : ** **B**

**Explanation : **

Let B be turned off after x minutes. Then,

Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1.

x (2/75 + 1/45) + (30 – x). 2/75 = 1

11x/225 + (60 -2x)/75 = 1

11x + 180 – 6x = 225.

x = 9.

**Question : 5** A pump can fill a tank with water in 2 hours. Because of a leak, it took 7/3 hours to fill the tank. The leak can drain all the water of the tank in:

A. 13/3

B. 7

C. 8

D. 14

**Show Answer**

**Correct Answer : ** **D**

**Explanation : **

Work done by the leak in 1 hour = (1/2) – (3/7)

= 1/14

Leak will empty the tank in 14 hrs