A Bath can be Filled by the Cold Water Pipe in 10 Min and by Hot Water GMAT Problem Solving

Question: A bath can be filled by the cold water pipe in 10 min and by hot water in 15 min (independently each). A person leaves the bathroom after turning on both the pipes simultaneously and returns at the moments when the bath should be full. Finding, however, that the waste pipe has been open he now closes it. In 4 min more, bath is full. In what time would be the waste pipe empty it?

1. 9 min
2. 12 min
3. 14 min
4. 15 min
5. 16 min

“A bath can be filled by the cold water pipe in 10 min and by hot water in 15 min (independently each). A person leaves the bathroom after turning on both the pipes simultaneously and returns at the moments when the bath should be full. Finding, however, that the waste pipe has been open he now closes it. In 4 min more, bath is full. In what time would be the waste pipe empty it?”- 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.

Solution and Explanation:

Approach Solution (1):

There is only one solution to the problem.

Work done by the cold water pipe in 1 minute =\(\frac{1}{10} \)

Work done by the hot water pipe in 1 minute =\(\frac{1}{15} \)

Work done together in 1 minute = \(\frac{1}{10} \)+ \(\frac{1}{15} \)=\(\frac{1}{6} \)

Time taken to fill when both are open = 6 minutes

He returns at the time when the bath should have been full, means that he returns in 6 minutes but finds that the waste pipe also has been opened for 6 minutes.

After he closes the waste pipe, it takes 4 more minutes to fill the tub

Let the waste pipe empty the bath in x minutes.

Work done by the cold pipe in 10 minutes (6 + 4) =\(\frac{10}{10} \)= 1

Work done by hot pipe in 10 minutes =\(\frac{10}{15} \)=\(\frac{2}{3} \)

Work done by waste pipe in 6 minutes =\(\frac{6}{x} \)

Sum of fractions of work done by each = 1

1 +\(\frac{2}{3} \) +\(\frac{6}{x} \) = 1

\(\frac{2}{3} \)=\(\frac{6}{x} \)

x = 9 minutes

Correct Answer: A

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