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3 pipes A, B and C will fill an empty reservoir in four hours, five hours and half dozen hours. There is a hole with in the tank, which might empty a full tank in eight hours. Initially, The tank is empty. Pipe A and B are opened. They are closed after half an hour. C is currently opened and allowed to run following one hour. calculate the entire time needed to fill the reservoir if all the 3 pipes are opened at the same time after the first one and a half hours. 

3 pipes A, B and C will fill an empty reservoir in four hours, five hours and half dozen hours. There is a hole with in the tank, which might empty a full tank in eight hours. Initially, The tank is empty. Pipe A and B are opened. They are closed after half an hour. C is currently opened and allowed to run following one hour. calculate the entire time needed to fill the reservoir if all the 3 pipes are opened at the same time after the first one and a half hours.  Correct Answer 3.11 hours

Given∶

Pipes A, B and C will fill an empty reservoir in four hours, five hours and half dozen hours.

Time taken to empty a full reservoir = 8 hours

Formula Used∶

Required Time = Work done in total hours / Work done in one hour

Calculation∶

Let the amount of work to be done to either fill an empty reservoir or empty a full reservoir be the 

LCM of ( 4,5,6,8) = 5 × 8 × 3 = 120 units

Work done by pipe A in one hour = 120/4 = 30 units

Work done by pipe B in one hour = 120/5 = 24 units

Work done by pipe C in one hour = 120/6 = 20 units

Work done by the hole in one hour = 120/8 = 15 units

Work done in the first one and a half hours = 15 + 12 + 20 - (3/2) × 15 = 47 - 22.5 = 24.5 units

Remaining work = 120 - 24.5 = 95.5 units 

Work done by the pipes together in 1 hour when they are opened simultaneously = 30 + 24 + 20 - 15 = 59 units

So, time required to fill the remaining reservoir = 95.5/59 = 1.61 hrs

So, total time required to fill the empty reservoir = 1.5 + 1.61 = 3.11 hours

∴ If takes 3.11 hours to fill the reservoir.

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