Hoses X and Y simultaneously fill an empty swimming pool that has a capacity of 50,000 liters. If the flow in each hose is independent of the flow in the other hose, how many hours will it take to fill the pool?

(1) Hose X alone would take 28 hours to fill the pool.

(2) Hose Y alone would take 36 hours to fill the pool.

Data Sufficiency

Question: 47

Category: Arithmetic Arithmetic operations

Page: 156

Difficulty: 600

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The answer is C. The solution is as follows.

1.(1) Hose X alone would take 28 hours to fill the pool - Insufficient as we are not aware at what rate the other hose fills the pool (Its like when two persons are doing the work we cant calculate how much time it takes to complete as we donot know the other persons working capability)

2.(2) Hose Y alone would take 36 hours to fill the pool. -- Insufficient

Now considering both 1 & 2 we know what rate both hose fill and will be sufficient to answer the question.

The quantitative solution is as follows.

Hose X fills tank in 28 hours so it fills 1/28 of the tank in an hour.

Hose Y fills tank in 36 hours so it fills 1/36 of tank in an hour.

they both together fills (1/28) +(1/36) =(16/252) =4/63. i.e they together fill 4/63 of tank in an hour.

To fill entire tank simultaneously they take 63/4 hours .

Hope only concept is sufficient to answer the question

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