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Two inlet pipes A and B can fill an empty cistern in 35 hours and 52.5 hours respectively while Pipe C is an outlet pipe that can drain the filled cistern in 17.5 hours. When the cistern is full Pipe C is left open for an hour, then closed and Pipe A is opened for an hour, closed and Pipe B is opened for an hour. The process continues till the cistern is empty. How many hours will it take for the filled cistern to be emptied?

Two inlet pipes A and B can fill an empty cistern in 35 hours and 52.5 hours respectively while Pipe C is an outlet pipe that can drain the filled cistern in 17.5 hours. When the cistern is full Pipe C is left open for an hour, then closed and Pipe A is opened for an hour, closed and Pipe B is opened for an hour. The process continues till the cistern is empty. How many hours will it take for the filled cistern to be emptied? Correct Answer 298

Pipes A and B can fill the cistern in 35 and 52.5 hours respectively.

Therefore,

part filled by pipe A in 1 hour = 1/35

part filled by pipe B in 1 hour = 1/52.5

Part emptied by pipe c in 1 hour = 1/17.5

Now,

Work done by all three pipes in 3 hours = -1/17.5 + (1/35 + 1/52.5)

⇒ -1/105 (negative sign indicates that in 3 hours pipes can empty 1/105 part of the cistern)

Time required by all the three pipes to empty 99/105 part of the cistern = 99 × 3 = 297 hours.

The remaining 6/105 part of the cistern will be emptied by pipe C in 1 hour.

∴ Total time taken to empty the tank = 297 + 1 = 298 hours

Additional Information

Person

The cistern can be filled in hours

LCM of 35, 52.5 and 17.5

 Efficiency

A

35

              

+5.55

B

52.5

194.25

+3.7

C

17.5

 

-11.1

Cistern emptied in 3 hour

 

 

 -1.85

It is started with pipe C

Pipe C can empty 11.1 units in 1 hour

194.25 - 11.1 = 183.15

183.15 is emptied in (183.15/11.1) = 99 

Total time = 99 × 3 + 1 = 298 hours

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