Pipes and Cisterns - Quant/Math - CAT 2009
Question 4 the day:
July 29, 2002
The question for the day is a pipes and cisterns problem.
- Pipe A usually fills a tank in 2 hours. On account of a leak at the bottom of the tank, it takes pipe A 30 more minutes to fill the tank. How long will the leak take to empty a full tank if pipe A is shut?
| (1) |
2 hours 30 minutes |
|
(2) |
5 hours |
|
(3) |
4 hours |
|
(4) |
10 hours |
Correct Answer - (4)
Solution:
Pipe A fills the tank normally in 2 hours. Therefore, it will fill ½ of the tank in an hour.
Let the leak take x hours to empty a full tank when pipe A is shut. Therefore, the leak will empty  of the tank in an hour.
The net amount of water that gets filled in the tank in an hour when pipe A is open and when there is a leak =  of the tank. — (1)
When there is a leak, the problem states that Pipe A takes two and a half hours to fill the tank. i.e.  hours. Therefore, in an hour,  of the tank gets filled. – (2)
Equating (1) and (2), we get  =>  => x = 10 hours.
The problem can also be mentally done as follows.
Pipe A takes 2 hours to fill the tank. Therefore, it fills half the tank in an hour or 50% of the tank in an hour.
When there is a leak it takes 2 hours 30 minutes for the tank to fill. i.e hours to fill the tank or or 40% of the tank gets filled.
On account of the leak, (50 - 40)% = 10% of the water gets wasted every hour. Therefore, the leak will take 10 hours to drain a full tank.
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