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Pipes P and Q fill a cistern in 12 minutes when operated together, Q and R fill it in 20 minutes when operated together and P and R fill it in 15 minutes when operated together. In how many minutes can all 3 pipes fill the cistern if operated together?

Pipes P and Q fill a cistern in 12 minutes when operated together, Q and R fill it in 20 minutes when operated together and P and R fill it in 15 minutes when operated together. In how many minutes can all 3 pipes fill the cistern if operated together? Correct Answer 10 minutes

Given:

P + R = 15 min

P + Q = 12 min

Q + R = 20 min

Calculation:

LCM of 15, 12, 20 = 60 unit (assume the total quantity of the tank)

Working together can fill the tank in:

Efficiency of P + R = 60/15 = 4 units/min

Efficiency of P + Q = 60/12 = 5 units/min

Efficiency of Q + R = 60/20 = 3 units/min

Efficiency of all three cistern when work together =

Adding all the three equation
2(P + Q + R) = 12

P + Q + R = 6

Total work can be completed in 60/6 = 10 mins

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