Question
In what time would a Cistern be filled by three pipes whose diameter are 2cm, 8/3 cm and 4cm running together, where the largest pipe alone fill it in 183 minutes. The amount of water flowing in by each pipe being proportional to the square of diameter?
Solution
1st Pipe 2nd Pipe 3rd Pipe Diameter 2 8/3 4 6 8 12 3 : 4 : 6 Efficiency proportional to the Square of the diameter 9 : 16 : 36 Total efficiency = 9 + 16 + 36 = 61 Pipe 3rd can fill the cistern in 183 minutes (given) Therefore, the capacity of the Tank = (36 × 183) = 6588 Now, the Time taken by all pipes together = 6588/61 = 108 minutes
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