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[kamalakarthi]

Hi, In the attached question, I tried to take common value as 24 litres and then I calculated the pipe can drain 6 litres in an hr so when the question says that the tank is emptied in 6 hrs , I calculated the capacity as 36 litres. Is this approach right ? or Is there a better approach to this question. Can you please help.

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Hi kamalakarthi,

Unfortunately, the math that you describe is not correct. This question can be solved in a variety of ways: algebraically, by TESTING THE ANSWERS or by using the difference in the two rates to figure out the capacity of the pool...

Based on the information in the prompt, there are two situations we have to consider:
1) It takes a pipe 4 hours to drain a full pool.
2) It take the same pipe 6 hours to drain that full pool when an additional 3 liters of water/hour is entering the pool (while it's being drained). This means that during those 6 hours of rain, another (6)(3) = 18 liters of water is being put INTO the pool.

At this point, you might recognize that those extra 18 liters of water will increase the time it takes to drain the pool by 2 hours. Thus, every 2 hours of 'drain time' accounts for 18 liters of water. The first sentence tells us that it takes 4 hours to drain the pool (when it's NOT raining) - so that 4 hours must account for double the water that the 2 hours accounts for... Thus, 4 hours of drain time = (2)(18) = 36 liters of water.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[Jay@ManhattanReview]

Hi, In the attached question, I tried to take common value as 24 litres and then I calculated the pipe can drain 6 litres in an hr so when the question says that the tank is emptied in 6 hrs , I calculated the capacity as 36 litres. Is this approach right ? or Is there a better approach to this question. Can you please help.

Hi kamalakarth,

It can also be solved in the following way.

Say the time taken to drain, working alone, is a hours and the time taken by rain to fill, working alone, is b hours. Thus, it takes 6 hours for the pool to empty if rain and drain work together.

Thus, 1/a - 1/b = 1/6

=> 1/4 - 1/b = 1/6

=>1/b = 1/4 - 1/6 = 1/12

=> b = 12 hours

=> Capacity of the pool= 12*(Rain inflow rate) = 12*3 = 36 liters

The correct answer: D

Hope this helps!

Relevant book: Manhattan Review GMAT Word Problems Guide

-Jay
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[Scott@TargetTestPrep]

Hi, In the attached question, I tried to take common value as 24 litres and then I calculated the pipe can drain 6 litres in an hr so when the question says that the tank is emptied in 6 hrs , I calculated the capacity as 36 litres. Is this approach right ? or Is there a better approach to this question. Can you please help.

Solution:

We can let c = the capacity of the pool. We see that the rate of the pipe emptying the pool is c/4 when the pool is full and it’s not raining, and that the rate of the pipe emptying the pool is c/6 when the pool is full and it’s raining. We can create the following equation:

c/4 - 3 = c/6

Multiplying the equation by 12, we have:

3c - 36 = 2c

c = 36

Alternate Solution:

Let r be the number of hours it would take the rain to fill the empty pool. Then, in one hour, the rain fills 1/r of the pool and the pipe empties 1/4 of the pool. Working together, the pool is emptied in 6 hours or, equivalently, 1/6 of the pool is emptied in one hour. Thus, we can create the following equation:

1/4 - 1/r = 1/6

Let’s multiply each side by 12r:

3r - 12 = 2r

r = 12

Thus, it would take the rain 12 hours to fill the empty pool. Then, since rain adds 3 liters of water to the pool each hour, the capacity of the pool is 12 x 3 = 36 liters.

Answer: D