Q. Pipes A and B are inlet pipes and the ratio of the efficiency of pipe A to pipe B is 2:3 and pipe C can empty the tank in 96 minutes. If pipes A, B and C opened together, after 9 minutes pipe C closed and pipes A and B together to fill the remaining tank in 12 minutes, then find the time taken by pipe A alone to fill the tank?
a) 48 minutes
b) 66 minutes
c) 32 minutes
d) 72 minutes
e) None of these
Sol:
Let the time taken by pipe A alone to fill the tank
= 1/3x
And the time taken by pipe B alone to fill the tank
= 1/2x
(1/3x + 1/2x – 1/96) * 9 + (1/3x + 1/2x) * 12 = 1
9/3x + 9/2x – 9/96 + 12/3x + 12/2x =1
18/6x + 27/6x + 24/6x + 36/6x = 1 + 9/96
105/6x = 105/96
x = (105 * 96)/(105 * 6)
x = 16
The time taken by pipe A alone to fill the tank = 3
* 16 = 48 minutes
