A bath can be filled by the cold water pipe in 10 min and by hot water

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