Question
Pipe βAβ and pipe βBβ can fill a cistern in 30
minutes and 10 minutes respectively. Pipe βCβ alone can empty the cistern in 12 minutes. If all three pipes are opened together then what is the time taken to fill 50% of the cistern?Solution
Let the capacity of the cistern = 60 units Then, efficiency of pipe βAβ = 60/30 = 2 units/minute Efficiency of pipe βBβ = 60/10 = 6 units/minute Efficiency of pipe βCβ = 60/12 = 5 units/minute So, combined efficiency of pipes βAβ, βBβ and βCβ = 2 + 6 β 5 = 3 units/minute 50% of the cisternβs capacity = 30 units Therefore, time taken by all 3 pipes together to fill 50% of the cistern = 30/3 = 10 minutes
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