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Two inlet pipes A & B can fill an empty cistern in 12 hours & 36 hours respectively while Pipe C is an outlet pipe that can drain the filled cistern in 6 hours. When the cistern is full Pipe C is left open for an hour, then closed & 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 & B can fill an empty cistern in 12 hours & 36 hours respectively while Pipe C is an outlet pipe that can drain the filled cistern in 6 hours. When the cistern is full Pipe C is left open for an hour, then closed & 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 46

Pipes A and B can fill the cistern in 12 and 36 hours respectively.

Therefore,

part filled by pipe A in 1 hour = 1/12.

part filled by pipe B in 1 hour = 1/36.

Part emptied by pipe c in 1 hour = 1/6.

Therefore,

Work done by all three pipes in 3 hours = - 1/6 + (1/12 + 1/36)

⇒ - 1/18 (negative sign indicates that pipes will drain the tank)

So,  in 3 × 15 = 45 hours  = (- 1/18) × 15 = - 5/6 part

Next hour by pipe C = - 5/6 - 1/6 = -1 

The time required by all the three pipes to empty the cistern = 45 + 1 = 46 hours. 

  

Concept used:

total work = time × efficiency

Calculation:

work time efficiency
A 12 hrs 36/12 = 3
B 36 hrs 36/36 = 1
C 6 36/6 = (-6)
Total work (LCM of time) 36  

The efficiency of C is taken negatively as it is the emptying pipe.

In the first hour amount of water emptied by C = 6 units

in the second hour amount of water filled by A = 3 units

In the third hour amount of water filled by B = 1 unit

Totally, in three hours amount of water emptied = -6 + 3 + 1 = 2 units

In 3 hrs → 2 units

in 3 × 15 hours = 45 hours → 2 × 15 = 30 units emptied

Now C has to do the next 1-hour work. It will empty 6 units in the next hour.

Thus, in the next one hour, the cistern will be empty.

So, total time taken to empty the cistern = 45 + 1 = 46 hours.

∴ Time taken to empty the cistern is 46 hours.

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