A pipe can fill an empty tank in 8 h. After it is kept open for 2 h, another pipe which can fill the tank in 6 h is opened. In how many more hours will the tank be filled?

Options

A. `(18)/(7)h`
B. `(19)/(7)h`
C. `(19)/(9)h`
D. `(18)/(8)h`

Answer

A

Explanation

Part of the tank filled in 2h `=(1)/(8) xx 2 = (1)/(4).`
The part of tank to be filled. `=1-(1)/(4) = (3)/(4).`
Part of tank filled in 1 h by both of the pipes = `(1)/(8) + (1)/(6) = (7)/(24).`
`therefore " Time taken to fill "(3)/(4)` th of the tank by both the pipes.
`=(3)/(4) xx (24)/(7) = (18)/(7)`h
Hence, the correct option is (a).