Two pipes A and B work alternatively with a third pipe C to fill a swimming pool Working alone A B a...........

Quant (SSC) Pipes&cistern

Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.

7 hours 14 minutes

6 hours 54 minutes

5 hours 14 minutes

8 hours 54 minutes

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Explanation:

Let the capacity of the pool be LCM (10, 20, 15) = 60 units.
=> Efficiency of pipe A = 60 / 10 = 6 units / hour
=> Efficiency of pipe B = 60 / 20 = 3 units / hour
=> Efficiency of pipe C = 60 / 15 = 4 units / hour
=> Efficiency of pipe A and pipe C working together = 10 units / hour
=> Efficiency of pipe B and pipe C working together = 7 units / hour
=> Pool filled in first hour = 10 units
=> Pool filled in second hour = 7 units
=> Pool filled in 2 hours = 10 + 7 = 17 units
We will have 3 cycles of 2 hours each such that A and C, and, B and C work alternatively.
=> Pool filled in 6 hours = 17 x 3 = 51 units
=> Pool empty = 60 – 51 = 9 units
Now, these 9 units would be filled by A and C working together with the efficiency of 10 units / hour.
=> Time required to fill these 9 units = 9/10 hour = 0.9 hours = 54 minutes
Therefore, total time required to fill the pool = 6 hours 54 minutes