An inlet pipe can fill an empty tank in \(4\frac{1}{2}\) hours while an outlet pipe drains a completely filled tank in \(7\frac{1}{5}\) hours. The tank is initially empty. and the two pipes are alternately opened for an hour each, till the tank is completely filled, starting with the inlet pipe. In how many hours will the tank be completely filled?

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Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 21 Jul 2023 Shift 2)

Answer 1

Given:

An inlet pipe can fill an empty tank in \(4\frac{1}{2}\) hours while an outlet pipe drains a completely filled tank in \(7\frac{1}{5}\) hours.

Concept used:

Efficiency = (Total work / Total time taken)

Efficiency = work done in a single day

Calculation:Time taken by A = 9/2 hours

Time taken by B = 36/5

Capacity of tank = LCM(9/2, 36/5) = 36 units

Efficiency of A = 36/(9/2) = 8 units

Efficiency of B = 36/(36/5) = - 5 units

tank filled in 2 hours = 8 - 5 = 3 units

tank filled in 20 hours = 30 units

and

Please note that after 20 hours, the remaining capacity = 6 units

Now in the 21st hour, pipe A will work and fill the tank so no need to add time after that.

Time taken by pipe A to fill 6 units = 6/8 = 3/4 hours

So,

Total time taken = 20 + 3/4 = \(20\frac{3}{4}\) hour

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