**Question:**

*A* and *B* can do a piece of work in 6 days and 4 days respectively. A started the work; worked at it for 2 days and then was joined by *B*. Find the total time taken to complete the work.

**Solution:**

A can do a work in 6 days, and B can do the same work in 4 days.

$\therefore$ Work done by A in 2 days $=\frac{2}{6}=\frac{1}{3}$

Remaining work $=1-\frac{1}{3}=\frac{2}{3}$

$\therefore$ Work done by $(\mathrm{A}+\mathrm{B})$ in 1 day $=\left(\frac{1}{6}+\frac{1}{4}\right)$

$=\frac{2+3}{12}=\frac{5}{12}$

$\because \frac{5}{12}$ th work is done by A and B in 1 day.

$\therefore \frac{2}{3}$ rd work will be done by A and B in $\left(\frac{12}{5} \times \frac{2}{3}\right)$ days or $\frac{8}{5}$ days.

$\therefore$ Total time taken $=\left(\frac{8}{5}+2\right)$ days $=\frac{18}{5}$ days $=3 \frac{3}{5}$ days