A cistern can be filled by two pipes in 8 minutes and 10 minutes, separately. Both the pipes are opened together for a certain time, but due to an obstruction, only 5/8 of the full quantity of water flowed through the former pipe and 3/5 through the latter pipe. However, the obstruction was suddenly removed, and the cistern was filled in 3 minutes from that moment. How long did it take before the full flow began?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. minutes.
Let the total work to be done (LCM of 8 and 10) be 40 units.
Efficiency of first pipe = 5 units/minute
Efficiency of second pipe = 4 units/minute
Water flow from first pipe after obstruction = 5 × (5/8) = 25/8 units/minute
Water flow from second pipe after obstruction = 4 × (3/5) = 12/5 units/minute
Work done by both pipes in last 3 minutes = (5 + 4) × 3 = 27 units
Remaining work = 40 - 27 = 13 units
Now, required time = 13/[25/8 + 12/5]
⇒ (13 × 40)/221
⇒ 40/17 = minutes