Two pipes A and B can fill a tank in 12 minutes and 24 minutes, respectively, while a third pipe C can empty the full tank in 32 minutes. All the three pipes are opened simultaneously. However, pipe C is closed 2 minutes before the tank is filled. In how much time (in minutes) will the tank be full?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 10.
Total work = LCM of (12, 24, 32) = 96 units.
Efficiency of A = 96/12 = 8 units/minutes.
Efficiency of B = 96/24 = 4 units/minutes.
Efficiency of C = 96/32 = 3 units/minutes.
Let the tank fill in 't' minutes.
Work done by A = 8 × t = 8t.
Work done by B = 4 × t = 4t.
Work done by C in (t - 2) minutes = 3(t - 2)
8t + 4t - 3t + 6 = 96
9t = 90
t = 90/9 = 10 minutes.