Question

Two pipes P and Q can fill a cistern in 36 and 48 minutes respectively. Both pipes are opened together, after how many minutes should Q be turned off, so that the cistern be fill in 24 minutes?
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Answer 1

$Time \: taken \: by \: P : 36 \: minutes$

$work \: done \: in \: 1 \: min = \frac{1}{36}$

$In \: 24 \: min, \: work \: done \: by \: P:$

$24 \times \frac{1}{36} = \frac{24}{36} = \: \frac{2}{3}$

$Remaining \: part \: = 1 - \frac{2}{3} = \: \frac{1}{3}$

$1 \: full \: part \: is \: filled \: by \: Q \: in \: 48 \: minutes$

$</p><p>⅓ \: part \: will \: be \: filled \: by \: it \: in \: \frac{48}{3} = 16 \: minutes.$

$So, \: Q \: must \: be \: stopped \: after \: 16 \: minutes.$