In what time would a cistern be filled by three pipes whose diameters are 1cm 2 cm and 3 cm running ...........

Quant (SSC) Pipes&cistern

In what time would a cistern be filled by three pipes whose diameters are 1cm, 2 cm and 3 cm running together, when the largest pipe alone can fill the tank in 21 minutes? The amount of water flowing through the pipe is directly proportional to the square of its diameter.

10.5 minutes

11.5 minutes

12.5 minutes

13.5 minutes

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Explanation:

More the diameter more will be the water flowing through it and less will be the time taken.
Means bigger pipe will take less time to fill the tank
So, for 1 cm time, (1^2)/(3^2) = 21/t, we get t = 189
For 2 cm time, (2^2)/(3^2) = 21/t. We get t = 189/4
So total time = 1/21 + 1/189 + 4/189 = 2/27
So total time = 13.5 minutes