A water tank is two-fifth full. Pipe A can fi | vedclass

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(A) Part of the tank filled by pipe $A$ in $1$ minute $= \frac{1}{10}$.Part of the tank emptied by pipe $B$ in $1$ minute $= \frac{1}{6}$.Since pipe $

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$6$ minutes to empty

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(A) Part of the tank filled by pipe $A$ in $1$ minute $= \frac{1}{10}$.Part of the tank emptied by pipe $B$ in $1$ minute $= \frac{1}{6}$.Since pipe $B$ empties faster than pipe $A$ fills,the net effect when both are open is emptying the tank.Net part of the tank emptied in $1$ minute $= \frac{1}{6} - \frac{1}{10} = \frac{5 - 3}{30} = \frac{2}{30} = \frac{1}{15}$.This means the tank is emptied at a rate of $\frac{1}{15}$ of the total capacity per minute.Since the tank is currently $\frac{2}{5}$ full,the time required to empty this $\frac{2}{5}$ portion is:Time $= \frac{	ext{Volume to be emptied}}{	ext{Rate of emptying}} = \frac{2/5}{1/15} = \frac{2}{5} 	imes 15 = 6$ minutes.Therefore,it will take $6$ minutes to empty the tank.

$A$ water tank is two-fifth full. Pipe $A$ can fill a tank in $10$ minutes,and pipe $B$ can empty it in $6$ minutes. If both the pipes are opened,how long will it take to empty or fill the tank completely?

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