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CAT 2018 [SLOT 1] Quant Question with Solution 02

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?

Show Answer
Correct Answer: 10

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

As per the first condition, 

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

Similarly, 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

Therefore, the capacity of the tank = (6x - 5y) × 6 = (7.5y - 5y) × 6 = 15y lts

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

Hence, the required time = 15y/1.5y=10 hours.


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