Pipes A and B can fill a tank in 12 hours and 16 hours respectively and pipe C can empty the full tank in 24 hours. All three pipes are opened toghether, but after 4 hours pipe B is closed. In how many hours, the empty tank will be completely filled?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e 18.
Given:
Pipes A and B can fill a tank in 12 hours and 16 hours respectively and pipe C can empty the full tank in 24 hours.
Explanation:
Let the total capacity of the tank be LCM of (12, 16, 24) = 48 units
Efficiency of A = 4 units/hour
Efficiency of B = 3 units/hour
Efficiency of C = - 2 units/hour
For 4 hours all pipes are opened together So, they filled the tank = (4 + 3 - 2) × 4
⇒ 5 × 4 = 20 units
Remaining capacity of the tank (48 - 20) = 28 units
Time taken by A and C to fill the remaining tank = 28/(4 - 2)
⇒ 28/2 = 14 hours
So, the total time take = 4 + 14 = 18 days