Question

$A$ can do a work in $6$ days and $B$ can do it in $8$ days, they worked together for $2$ days and then $B$ left the work. How many days will $A$ require to finish the work?

Answer 1

Given,

$A$ can do a work in = $6$ days

$A$’s, $1$ day work $=\frac{1}{6}$

$B$ can do a work in = $8$ days

$B$’s, $1$ day work $=\frac{1}{8}$

Both $(A+B)$’s $1$ day work $=\frac{1}{6}+\frac{1}{8}$

$=\frac{4+3}{24}$$=\frac{7}{24}$

Both $(A+B)$’s $2$ day work $=2\times \frac{7}{24}$

$=\frac{7}{12}$

So, the remaining work $=1-\frac{7}{12}$$=\frac{12-7}{12}$$=\frac{5}{12}$

Now,

It is given that,

$A$ can do a work in $6$ days

A can do $\frac{5}{12}$ work in $=6\times \frac{5}{12}$ days

$=\frac{5}{2}$ days

$=2\frac{1}{2}$ days

$\therefore A$ can finish the work in $2\frac{1}{2}$ days.