Pipes A and B can fill a tank in 20 hours and 30 hours, respectively, and pipe C is an outlet pipe. If all three pipes are opened together, it takes 1 hour more than the time taken by A and B together to fill the tank. A and B are opened together for 7 hours, then both are closed, and C is opened. Now C can empty the tank in:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 70 hours.
Combined rate of A and B = 1/20 + 1/30 = 1/12
Time for A + B to fill the tank = 12 hours
Time for all three pipes = 12 + 4/3 = 40/3 hours
Combined rate (A + B - C) = 3/40
1/12 - 1/C = 3/40
⇒ 1/C = 1/12 - 3/40 = 1/120
Amount filled in 7 hours by (A + B) = 7 × (1/12) = 7/12
Time for C to empty = (7/12)/(1/120) = 70 hours