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Bunuel
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A bath can be filled by the cold water pipe in 10 min and by hot water 03 Dec 2020, 01:00
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66% (02:59) correct 34% (02:23) wrong based on 297 sessions

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A bath can be filled by the cold water pipe in 10 min and by hot water pipe in 15 min (independently each). A person leaves the bathroom after turning on both 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?

A. 9 min
B. 12 min
C. 14 min
D. 15 min
E. 16 min
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A bath can be filled by the cold water pipe in 10 min and by hot water 05 Dec 2020, 03:29
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Bunuel
A bath can be filled by the cold water pipe in 10 min and by hot water pipe in 15 min (independently each). A person leaves the bathroom after turning on both 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?

A. 9 min
B. 12 min
C. 14 min
D. 15 min
E. 16 min
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Work done by the cold water pipe in 1 minute = \(\frac{1}{10}\)

Work done by the cold 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 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


Option A

Arun Kumar
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A bath can be filled by the cold water pipe in 10 min and by hot water 07 Dec 2020, 02:19
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CrackVerbalGMAT
Sum of fractions of work done by each = 1

1+2/3+6/x=1
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Arun, the waste pipe will remove the water, hence it should be substracted from the equation, in the following way:

1+2/3-6/x=1
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A bath can be filled by the cold water pipe in 10 min and by hot water 10 Dec 2020, 08:29
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Bunuel
A bath can be filled by the cold water pipe in 10 min and by hot water pipe in 15 min (independently each). A person leaves the bathroom after turning on both 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?

A. 9 min
B. 12 min
C. 14 min
D. 15 min
E. 16 min
Show more

So for the last 4 minutes only the input pipes are operating.

Work done by both the input pipes in last 4 minutes \(\frac{4}{10}+\frac{4}{15}=\frac{2}{3}\)

Hence work done before that is \(\frac{1}{3}\)

So both input and one output pipe was open for 6 minutes and work done was \(\frac{1}{3}\).
If \(\frac{1}{3}\) work in 6 minutes so whole work in 18 minutes.
Hence Both input and one output pipe can do the whole work in 18 minutes.

We can form an equation.
\(\frac{1}{6}\) -\(\frac{1}{x}\) =\(\frac{1}{18}\)

Where \(x\) is the time taken for the output pipe to empty the whole bath alone.

On solving we get \(x=9\)

Hope it's clear.
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A bath can be filled by the cold water pipe in 10 min and by hot water 30 Oct 2022, 18:57
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The two pipes, working simultaneously and independently of each other, would have a combined rate of:

(1/10) + (1/15) = 1/6

Where the job is to fill the sink and we let the job = 1

1/6 ——- represents the fact that the two could fill 1 sink and 6 minutes.

The person walks in after those 6 minutes when the sink should have been filled.

The Drainage Pipe is turned off, and the two pipes need 4 more minutes to finally finish the job.

This means that the two pipes were only able to do 2 minutes of the 6 minutes of positive work.

In other words, they only accomplished filling (2/6) or (1/3) of the entire sink in those 6 minutes.

Let the Rate of the Drainage Pipe be = (1/X)

Rate * Time = Work accomplished of 1/3rd of sink filled

(1/6 — 1/X) * (6) = (1/3)

1/X = (1/6) — (1/18)

1/X = 1/9

The Drainage Pipe could empty the 1 sink in 9 hours

*A* 9

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A bath can be filled by the cold water pipe in 10 min and by hot water 01 Jan 2026, 04:33
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