Discussion
3 pipes have diameters 2 cms, 3 cms and 4 cms. The ratio of water flowing through them is equal to ratio of the square of their diameters.The biggest pipe when open alone, can fill the entire pool in just 126 minutes. When all the pipes are opened together, the pool would be filled in how much time?
Answer: A
Flow varies as the square of the diameter, so the three pipes are in the ratio
\[ 2^{2} : 3^{2} : 4^{2} = 4 : 9 : 16 \]
The biggest carries 16 of the 29 parts and fills the pool in 126 minutes, so all three together work \( \tfrac{29}{16} \) times as fast:
\[ t = 126 \times \frac{16}{29} = \frac{2016}{29} \text{ minutes} \]
That is about 69.5 minutes - a little over half the 126, as expected when the flow nearly doubles.
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