Question

$A$ can finish a piece of work in $15$ days and $B$ can do it in $10$ days. They worked together for $2$ days and then $B$ goes away. In how many days will $A$ finish the remaining work?

Answer 1

$A$ can finish a piece of work in $=15$ days

$B$ can finish a piece of work in $=10$ days

$\therefore$ $A^{\prime }s$ $1$ day work $=\frac{1}{15}$

$B^{\prime }s$ $1$ day work $=\frac{1}{10}$

$(A+B{)}^{\prime }s$ $1$ day work $=\frac{1}{15}+\frac{1}{10}$

$=\frac{2+3}{30}=\frac{5}{30}=\frac{1}{6}$

$(A+B{)}^{\prime }s$ $2$ days work $=\frac{1}{6}\times 2=\frac{1}{3}$

Remaining work which will be done by $A$ alone

$=1-\frac{1}{3}=\frac{3-1}{3}=\frac{2}{3}$ [Whole work is considered as $1$]

$\therefore$ $A$ can finish $1$ work in $=15$ days

$A$ can finish $\frac{2}{3}$ work in $=15\times \frac{2}{3}$ days.

$=\frac{30}{3}$ days $=10$ days.