A pipe, working at full speed, can fill an empty cistern in 1 hour. However, during the first hour it worked at one-twelfth of its capacity, during the second hour at one-ninth of its capacity, during the third hour at one-sixth of its usual capacity, during the fourth hour at one- fourth of its usual capacity and during the fifth hour it was only one-third as efficient as it was supposed to be. A second pipe also displayed similar performance, but if it worked at full speed would have filled the empty cistern in 2 hours. Together with a drain pipe that drained water out of the tank at a constant rate, the empty cistern could be filled in 5 hours, all the three pipes working concurrently. How many hours will it take the drain pipe to empty the filled cistern if no other pipe was functioning during the time?

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A pipe, working at full speed, can fill an empty cistern in 1 hour. However, during the first hour it worked at one-twelfth of its capacity, during the second hour at one-ninth of its capacity, during the third hour at one-sixth of its usual capacity, during the fourth hour at one- fourth of its usual capacity and during the fifth hour it was only one-third as efficient as it was supposed to be. A second pipe also displayed similar performance, but if it worked at full speed would have filled the empty cistern in 2 hours. Together with a drain pipe that drained water out of the tank at a constant rate, the empty cistern could be filled in 5 hours, all the three pipes working concurrently. How many hours will it take the drain pipe to empty the filled cistern if no other pipe was functioning during the time?

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RRB ALP CBT I 14 Aug 2018 Shift 1 Official Paper

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Answer 1

Given:

Pipe 1 can fill the tank in 1 hour

Pipe 2 can fill the tank in 2 hours

Calculation:

Let the total work be 36x units

So, efficiency of Pipe 1 = 36x/1 = 36x units/h

Efficiency of pipe 2 = 36x/2 = 18x units/h

Let the efficiency of draining pipe be y

According to the question,

36x × (1/12) + 36x × (1/9) + 36x × (1/6) + 36x × (1/4) + 36x × (1/3) + 18x × (1/12) + 18x × (1/9) + 18x × (1/6) + 18x × (1/4) + 18x × (1/3) - 5y = 36x

⇒ 3x + 4x + 6x + 9x + 12x + 1.5x + 2x + 3x + 4.5x + 6x - 5y = 36x

⇒ 51x - 5y = 36x

⇒ 15x = 5y

⇒ y = 3x

So,, efficency of the draining pipe is 3x

So, required time = 36x/3x

⇒ 12 hours

∴ The required answer is 12.

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