Question

Two taps $A$ and $B$ can fill an overhead tank in $10$ hours and $15$ hours respectively. Both the taps are opened for $4$ hours and then $B$ is turned off. How much time will $A$ take to fill the remaining tank?

Answer 1

Time taken by $A$ to fill a tank $=10$ hours

$\therefore$ Quantity of tank filled by $A$ in $1$ hour = $\frac{1}{10}$ units

Similarly, Quantity of tank filled by $B$ in $1$ hour = $\frac{1}{15}$ units

Now, Quantity of tank filled by $A$ and $B$ together, in $1$ hour = $\frac{1}{10}$ units $+\frac{1}{15}=\frac{3+2}{30}=\frac{1}{6}$ units

Hence, Quantity of tank filled by $A$ and $B$ together, in $4$ hours = $4\times \frac{1}{6}=\frac{2}{3}$ units

Quantity of tank left to be filled = $1-\frac{2}{3}=\frac{1}{3}$ units

Therefore, time taken by $A$ to fill $\frac{1}{3}$ units of tank = $\frac{1}{3}\times 10=3\frac{1}{3}$ hours