Two pipes A and B can fill a tank in 10 hours and 30 hours respectively Due to a leak in the tank it...........

Quant (SSC) Pipes&cistern

Two pipes A and B can fill a tank in 10 hours and 30 hours respectively. Due to a leak in the tank, it takes 2.5 hours more to fill the tank. How much time would the leak alone will take to empty the tank ?

20 hours

25 hours

30 hours

35 hours

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Explanation:

Explanation: Let the capacity of the tank be LCM (10, 30) = 30 units
=> Efficiency of pipe A = 30 / 10 = 3 units / hour
=> Efficiency of pipe B = 30 / 30 = 1 units / hour
=> Combined efficiency of both pipes = 4 units / hour
Now, total time taken by A and B working together to fill the tank if there was no leak = 30 / 4 = 7.5 hours
=> Actual time taken = 7.5 + 2.5 = 10 hours
The tank filled by A and B in these 2.5 hours is the extra work done to compensate the wastage by the leak in 10 hours.
=> 2.5 hours work of A and B together = 10 hours work of the leak
=> 2.5 x 4 = 10 x E, where ‘E’ is the efficiency of the leak.
=> E = 1 unit / hour
Therefore, time taken by the leak alone to empty the full tank = 30 / 1 = 30 hours