GMAT Problem Solving - A Draining Pipe Can Empty a Pool in 4 Hours

Question: A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?

1. 9 liters
2. 18 liters
3. 27 liters
4. 36 liters
5. 45 liters

“A draining pipe can empty a pool in 4 hours. On a rainy day, when the pool is full, the draining pipe is opened and the pool is emptied in 6 hours. If rain inflow into the pool is 3 liters per hour, what is the capacity of the pool?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer

Approach Solution 1

Let the rate of the draining pipe be x liters per hour.
Then the capacity of the tank will be C = time * rate = 4x,
Now, when raining, the net outflow is x-3 liters per hour, and we are told that at this new rate the pool is emptied in 6 hours.
So, the capacity of pool = time * rate = 6 (x-3)
Thus, we have: 4x = 6 (x-3)
Thus after solving, we will get:
x = 9
Thus, C = 4x = 36

Correct option: D

Approach Solution 2

Given data: Drain rate = \(\frac{x}{4}\)

Also given: Drain rate + Inflow rate = \(\frac{x}{6}\)

i.e.,

\(\frac{x}{4}\)+ Inflow rate = \(\frac{x}{6}\)

i.e., Inflow rate = \(\frac{x}{12}\)

It’s given that, it takes 1 hr = to fill 3 liters

So, in 12 hours= we can fill 12 * 3 = 36 liters

Correct option: D

Approach Solution 3

Let x be the capacity of the tank 

Speed of water outflow in scenarios one – \(\frac{x}{4}\)

Speed of water outflow in scenarios one - \(\frac{(x+18)}{6}\) - add 6 * 3 = 18 hours for the additional water contributed by rain at 3 liters per hour

Equate both \(\frac{x}{4}\) = \(\frac{(x+18)}{6}\)

6x = 4(x+18)

x = 36

Correct option: D

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