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

Options

A. 6 minutes
B. 9 minutes
C. 3 minutes
D. 15 minutes

Answer

(b)

Explanation

Let 180 units be the capacity of tub
P and Q together can fill tank in `180/(18+12)=6 `min
`therefore` we can say,
Work done by 'R' in 6 min = work dons by (P&Q)
Together in 4 minutes
`rArr 6 cdot x = 4 xx (18+12)`
`rArr x= 20`
`therefore` R is doing 20 units of work in 1 minute
`therefore` requires `180/20=9` minutes to empty tank