Two pipes `P_(1) " and " P_(2)` can fill a tank in 6 h and 3 h, respectively. Both the pipes are opened simultaneously and pipe `P_(1)` is closed after 1 h.. Find the time taken by `P_(2)` to fill the remaining par of the tank (in hours).

Options

A. 1
B. `1(1)/(2)`
C. 2
D. `2(1)/(2)`

Answer

B

Explanation

Pipe `P_(1) " can fill " (1)/(6)` of the tank in 1 h.
Pipe `P_(2) " can fill " (1)/(3)` of the tank in 1 h.
Pipe `P_(1) " and " P_(2) " together can fill " ((1)/(6) + (1)/(3))` of the tank in 1 h.
The part of the tank to be filled = `1-((1)/(6) + (1)/(3))`
` = 1-((1+2)/(6)) = (6-3)/(6) = (3)/(6) = (1)/(2)`
Time taken by the pipe `P_(2) " to fill " (1)/(2)` of tank at the
`"rate of " (1)/(3) " per hour "=(((1)/(2)))/(((1)/(3))) = (1)/(2) xx (3)/(1) = 1(1)/(2)`h.
Hence, the correct option is (b).