**Question: **

A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?

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Correct Answer: 10

Let the rate of each filling pipes be 'x lts/hr' and the rate of each draining pipes be 'y lts/hr'.

According to the first condition,

Capacity of tank = (6x - 5y)×6..........(i)

From the second condition,

Capacity of tank = (5x - 6y) × 60.....(ii)

On equating (i) and (ii), we get

(6x - 5y) × 6 = (5x - 6y)×60

or, 6x - 5y = 50x - 60y

or, 44x = 55y

or, 4x = 5y

or, x = 1.25y

Capacity of the tank = (6x - 5y) × 6 = (7.5y - 5y) × 6 = 15y

Effective rate of 2 filling and 1 draining pipes = (2x - y) = (2.5y - y) = 1.5y

Time required = $\frac{\text{15y}}{\text{1.5y}}$hours = 10 hours.

Hence, 10 is the correct answer.

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