Two pipes A and B can fill a cistern in $$37\frac{1}{2}$$ minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
a) 5 min.
b) 9 min.
c) 10 min.
d) 15 min.
Answer: b
Explanation: Let B be turned off after x minutes.
Then, Part filled by (A + B) in x min. + Part filled by A in (30 – x) min. = 1
$$\eqalign{
& x\left( {\frac{2}{{75}} + \frac{1}{{45}}} \right) + \left( {30 – x} \right).\frac{2}{{75}} = 1 \cr
& \frac{{11x}}{{225}} + \frac{{ {60 – 2x} }}{{75}} = 1 \cr
& 11x + 180 – 6x = 225 \cr
& x = 9 \cr} $$
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