A water tank is $\frac{2}{5}$ th full. Pipe $A$ can fill the tank in 10 minutes and pipe $B$ can empty it in $6$ minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?

6

minutes to empty

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6

minutes to fill

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9

minutes to empty

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9

minutes to fill

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Solution

The correct option is A $6$ minutes to empty
Pipe $A$ in 1 minute fills $\frac{1}{10}$ part and pipe $B$ in 1 minute empties $\frac{1}{6}$ part.
$∴$ Work done by pipe $(A + B)$ in 1 min $= \frac{1}{10} - \frac{1}{6} = \frac{1}{15}$
$\Rightarrow \frac{1}{15}$ parts gets emptied in 1 min
$\Rightarrow \frac{2}{5}$ part is emptied in $15 \times \frac{2}{5}$ min $= 6$ min.

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A water tank is 25th full. Pipe A can fill the tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?

The correct option is A 6 minutes to emptyPipe A in 1 minute fills 110 part and pipe B in 1 minute empties 16 part.∴ Work done by pipe (A+B) in 1 min =110−16=115⇒115 parts gets emptied in 1 min⇒25 part is emptied in 15×25 min =6 min.

A water tank is $\frac{2}{5}$ th full. Pipe $A$ can fill the tank in 10 minutes and pipe $B$ can empty it in $6$ minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?