Question
A large cistern can be filled by
two pipes, P and Q, in 16 minutes and 24 minutes, respectively. Pipe R can empty the cistern in 32 minutes. How many minutes will it take to fill the cistern starting from empty if: i)Â Â Pipes P and R are used to fill 25% of the cistern, ii)Â Pipes Q and R are used to fill the next 25%, iii) Pipes P and Q are used to fill the remaining 50% of the cistern?Solution
ATQ, P - R = (1/16) - (1/32) = 1/32 32 minutes to fill full tank, To fill 25% of the tank => 32 × (1/4) = 8 minutes Q - R = (1/24) - (1/32) = 1/96 96 minutes to fill full tank, To fill 25% of the tank => 96×1/4 = 24 minutes P + Q = (1/16) + (1/24) = 5/48 48/5 minutes to fill full tank To fill 50% of the tank => (48/5) × (1/2) = 24/5 = 4.8 minutes Required total time = 8 + 24 + 4.8 = 36.8 minutes
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