[4 min] Two pipes P and Q can fill a cistern in 12 min and 16 min respectively. Simultaneously both the pipe

Two pipes P and Q can fill a cistern in 12 min and 16 min respectively. Simultaneously both the pipes are opened together, then after how much time Q should be closed so that tanks full in 9 min?

3.5 min

4 min

4.5 min

4.75 min

Explanation:

Part of the cistern filled by pipe P in 1 min = $\dfrac{1}{12}$
Part of the cistern filled by pipe Q in 1 min = $\dfrac{1}{16}$
Suppose Q should be closed after x minutes
i.e., Pipe P and Q will be open for initial x minutes then P will be open for another (9-x) min
x$\left(\dfrac{1}{12}+\dfrac{1}{16}\right)+(9-x)\dfrac{1}{12}$=1
$\dfrac{7x}{48}+\dfrac{9}{12}-\dfrac{x}{12}$=1
7x+36−4x=48
3x=12
x=4

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