Pipes P1 and P2 alone can fill a tank in 5 hours and 10 hours respectively. Pipe P3 alone can empty the same tank in 20 hours. Firstly, both pipes P1 and P2 are opened and after 1 hour pipe P3 is also opened. In how much total time (in hours) tank will be completely filled?
Show answer & explanation
Correct answer: A
Explanation
Given:
P1 = 5 hours, P2 = 10 hours, P3 = 20 hours (emptying)
According to the formula:
Work Rate = 1 / Time
P1 = 1/5, P2 = 1/10
Work done in the first 1 hour = 1/5 + 1/10 = 3/10
Remaining work = 7/10
Now, all three together:
1/5 + 1/10 − 1/20 = (4 + 2 − 1)/20 = 5/20 = 1/4
Time required for the remaining work = (7/10) ÷ (1/4) = 28/10 = 2.8
Total time = 1 + 2.8 = 3.8 = 19/5 hours