Pipe & Work Question Answers

Pipes and Cisterns - Quant/Math - CAT 2008

Question 4 the day: May 23, 2002

The question for the day is from the topic Pipes and Cisterns. The problems from the topic Pipes and Cisterns and Work and Time are very similar in nature. So, if you understand the nature of one of these types, you will be able to attempt the other quite comfortably.

Pipe A fills a tank of 700 litres capacity at the rate of 40 litres a minute. Another pipe B fills the same tank at the rate of 30 litres a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 litres a minute. If pipe A is kept open for a minute and then closed and pipe B is kept open for a minute and then closed and then pipe C is kept open for a minute and then closed and the cycle repeated, how long will it take for the empty tank to overflow?

(1)

42 minutes

(2)

14 minutes

(3)

39 minutes

(4)

None of these

Correct Answer - (4)

---

Solution

Pipe A fills the tank at the rate of 40 litres a minute. Pipe B at the rate of 30 litres a minute and Pipe C drains the tank at the rate of 20 litres a minute.

If each of them is kept open for a minute in the order A-B-C, the tank will have 50 litres of water at the end of 3 minutes.

After 13 such cycles, the tank will have 13 * 50 = 650 litres of water.
It will take 13 * 3 = 39 minutes for the 13 cycles to be over.

At the end of the 39^th minute, Pipe C will be closed and Pipe A will be opened. It will add 40 litres to the tank.

Therefore, at the end of the 40^th minute, the tank will have 650 + 40 = 690 litres of water.
At the end of the 40^th minute, Pipe A will be closed and Pipe B will be opened. It will add 30 litres of water in a minute.

Therefore, at the end of the 41^st minute, the tank will have 690 + 30 = 720 litres of water.
But then at 700 litres, the tank will overflow. Therefore, Pipe B need not be kept open for a full minute at the end of 40 minutes.

Pipe B needs to add 10 more litres of water at the end of 40 minutes. It will take 1/3rd of a minute to fill 10 litres of water.

Therefore, the total time taken for the tank to overflow = 40 minutes + 1/3 of a minute
or 40 minutes 20 seconds.