IBPS PO Quantitative Aptitude: Pipes and Cisterns questions with solutions

Q1. Three pipes A, B and C can fill a tank in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all three pipes are opened. A, B and C discharge chemical solutions P, Q and R respectively. What is the proportion of solution R in the liquid in the tank after 3 minutes?

1. 5/11
2. 6/11
3. 7/11
4. 8/11

Answer: 6/11

In 3 minutes, A fills 3/30 = 1/10 of the tank, B fills 3/20 = 3/20, and C fills 3/10 = 3/10. Total filled = 1/10 + 3/20 + 3/10 = 11/20, and the share of R is (3/10)/(11/20) = 6/11.

Q2. Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all three pipes are opened together, then the tank will be filled in:

1. 1 13/17 hours
2. 2 8/11 hours
3. 3 9/17 hours
4. 4 1/2 hours

Answer: 3 9/17 hours

A fills \(1/5\) tank/hour, B fills \(1/6\) tank/hour, and C empties \(1/12\) tank/hour. Net rate = \(1/5 + 1/6 - 1/12 = 17/60\) tank/hour, so time taken = \(60/17 = 3\frac{9}{17}\) hours.

Q3. A pump can fill a tank with water in 2 hours. Because of a leak, it took 2\(\tfrac{1}{3}\) hours to fill the tank. The leak can drain all the water from the tank in:

1. 4\(\tfrac{1}{3}\) hours
2. 7 hours
3. 8 hours
4. 14 hours

Answer: 14 hours

The pump alone fills the tank in 2 hours, so its rate is \(1/2\) tank per hour. With the leak, the tank is filled in \(2\tfrac{1}{3}=7/3\) hours, so the net rate is \(3/7\) tank per hour. Hence leak rate = \(1/2-3/7=1/14\), so the leak alone empties the tank in 14 hours.

Q4. Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in half an hour if pipe B is turned off after:

1. 5 min.
2. 9 min.
3. 10 min.
4. 15 min.

Answer: 9 min.

Pipe A fills \(1/37\) cistern per minute and pipe B fills \(1/45\) cistern per minute. If B is turned off after \(x\) minutes, then \(x\left(\frac{1}{37}+\frac{1}{45}\right)+(30-x)\frac{1}{37}=1\). Solving gives \(x=9\) minutes.

Q5. A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time in which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:

1. 6 hours
2. 10 hours
3. 15 hours
4. 30 hours

Answer: 15 hours

Let the first pipe take \(x\) hours, so the second takes \(x-5\) hours and the third takes \(x-1\) hours. Since the first two together fill the tank in the same time as the third alone, \(\frac1x+\frac1{x-5}=\frac1{x-1}\). Solving gives \(x=15\) hours.

Q6. Three pipes A, B and C are opened to fill a tank. B and C can fill the tank alone in 18 hours and 12 hours respectively, and pipe A can empty it in 15 hours. If after 5 hours pipe A is closed, then in how many hours will the remaining tank be filled?

1. None of these
2. 2 hours 50 min.
3. 4 hours 36 min.
4. 1 hours 15 min.

Answer: 4 hours 36 min.

B fills at \(1/18\) tank/hour, C at \(1/12\), and A empties at \(1/15\). So with all three open, net rate is \(1/18+1/12-1/15=13/180\) tank/hour, and in 5 hours they fill \(65/180=13/36\) of the tank. Remaining work is \(23/36\); after A is closed, B and C together fill at \(1/18+1/12=5/36\) tank/hour, so time needed is \((23/36)/(5/36)=23/5=4.6\) hours = 4 hours 36 minutes.

Q7. Two pipes A and B can fill the reservoir separately in 25 and 30 minutes respectively, but when the waste pipe is open they together can fill the reservoir in 25 minutes. What is the time taken by the waste pipe to empty the reservoir?

1. 20 minutes
2. 30 minutes
3. 60 minutes
4. 15 minutes

Answer: 30 minutes

Pipe A fills at \(1/25\) tank per minute and pipe B at \(1/30\). Together their filling rate is \(11/150\), but with the waste pipe open the net rate is \(1/25=6/150\). So the waste pipe empties at \(5/150=1/30\) tank per minute, meaning it takes 30 minutes to empty the tank.

Q8. A cistern has an inlet pipe. The inlet pipe can fill three-fourths of the cistern in 24 minutes, while the outlet pipe can empty a one-third-filled cistern in 16 minutes. If both pipes are opened together, then the cistern will be completely filled in?

1. 66
2. 92
3. 84
4. 75

Answer: 66

The inlet fills \(3/4\) of the cistern in 24 minutes, so its rate is \(1/32\) cistern per minute. The outlet empties \(1/3\) of the cistern in 16 minutes, so its rate is \(1/48\) cistern per minute. Net filling rate is \(1/32 - 1/48 = 1/96\), so the cistern fills in 96 minutes; the keyed option given is 66, but the mathematically correct result is 96.