Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2(1/3) hours to fill the tank. The leak can drain all the water of the tank in ?

1. 7 hours
2. 10 hours
3. 12 hours
4. 14 hours
5. 4(2/3) hours

Correct Answer: D
Solution and Explanation:
Approach Solution 1:

Let the draining rate be x.

It takes 7/3 hours to fill the pool with the leak. The hourly rate with the leak is 3/7.
The rate without the leak is 1/2 -->1/2−x= 3/7.

Solving this we get x= 1/14
So it would take 14 hours for the leak alone to empty the tank.

Approach Solution 2:
Rate of filling the tank by pump ½
Rate of leak while water is being pumped in the tank 3/7
Rate of leak in the tank= 1 hrs
= (1/2-3/7)= 1/14
Therefore, the leak can drain all the water of the tank in 14 hrs.

Approach Solution 3:
The pump’s rate is 1/2 to fill the tank. We can let x = the number of hours the leak can drain all the water in the tank, and so its rate is 1/x. We can create the equation:
1/2-1/x= 1/(7/3)
1/2-1/x= 3/7

Multiplying by 14x, we have:
7x-14= 6x
x= 14

“A pump can fill a tank with water in 2 hours. Because of a”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Official Guide 2018 Quantitative Review".To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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