Three pipe P, Q and R can fill a tank in 12 minutes, 18 minutes
and 24 minutes respectively. The pipe R is closed 12 minutes
before the tank is filled. In what time the tank is full?

Options

A. ` 8 5/13 hrs.`
B. `8 4/13 hrs.`
C. `7 4/13` hrs
D. `8 6/13 hrs`

Answer

(b)

Explanation

Let T is the time taken by the pipes to fill the tank
Let capacity of tank `= LCM of (12, 18, 24)=72` units
`therefore` P in 1 min can fill 6 units
Q in 1 min can fill 4 units
R in 1 min can fill 3 units
`therefore (10 t + 3 (t-12)=72`
`13 t= 108`
`rArr t = 8 4/13` hours