Question: There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes?

1. 5
2. 6
3. 7
4. 8
5. 9

Correct Answer: (C)

Solution and Explanation:

There is only one solution to this problem.

Approach Solution 1:
Let the number of fill pipes be = x

Therefore the number of drain pipes = 12 – x
Time taken by 1 fill pipe = 8 hours

Work done by 1 fill pipe in 1 hour = \(\frac{1}{8}\)

Work done by x fill pipes in 1 hour = \(\frac{x}{8}\)

Time taken by 1 drain pipe to empty = 6 hours

Work done by 1 drain pipe in 1 hour = \(\frac{1}{6}\)

Work done by x fill pipes in 1 hour = (12 – x) * \(\frac{1}{8}\) = \(\frac{12-x}{8}\)

Total time to fill the tank = 24 hours

Amount filled in 1 hour = \(\frac{1}{24}\)

Therefore \(\frac{x}{8}-\frac{12-x}{6}=\frac{1}{24}\)

\(\frac{3x – 4(12-x)}{24} = \frac{1}{24}\)

3x – 48 + 4x = 1
7x = 49
x = 7

“There are 12 pipes that are connected to a tank. Some of them are fill”- 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.

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