A tap A can fill a cistern in $8$ hours while tap B can fill it in $4$ hours. In how much times will the cistern be filled if both A and B are opened together?

2 h r s 30 m i n

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2 h r s 40 m i n

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2 h r s 50 m i n

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3 h r s

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Solution

The correct option is C $2 h r s 40 m i n$
Time taken by tap A to fill the cistern $= 8$ hours.
Work done by tap A in $1$ hour $= \frac{1}{8}$
Time taken by tap B to fill the cistern $= 4$ hours.
Work done by tap B in $1$ hour $= \frac{1}{4}$
Work done by $(\begin{matrix} A + B \end{matrix})$ in $1$ hour $= \frac{1}{8} + \frac{1}{4} = \frac{3}{8}$
Therefore, time taken by $(\begin{matrix} A + B \end{matrix})$ to fill the cistern $= \frac{8}{3}$ hours $= 2 h o u r s 40 m i n$ .

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