Concept: The question tests on application of Rates(Time and Work)
Work done by the cold water pipe in 1 minute = 1/10
Work done by the cold water pipe in 1 minute = 1/15
Work done together in 1 minute = 1/10+1/15=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) = 10/10 = 1
Work done by Hot pipe in 10 minutes = 10/15=2/3
Work done by waste pipe in 6 minutes = 6/x
Sum of fractions of work done by each = 1
x = 9 minutes