**Question:**

A, B and C can do a piece of work in 15, 12 and 20 days respectively. They started the work together, but C left after 2 days. In how many days will the remaining work be completed by A and B?

**Solution:**

Time taken by $\mathrm{A}=15$ days

Time taken by $\mathrm{B}=12$ days

Time taken by $\mathrm{C}=20$ days

Work $d$ by $\mathrm{A}$ in one day $=\frac{1}{15}$

Work done by $\mathrm{B}$ in one day $=\frac{1}{12}$

Work done by $\mathrm{C}$ in one day $=\frac{1}{20}$

Work done in one day by $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ together $=\frac{1}{15}+\frac{1}{12}+\frac{1}{20}=\frac{4+5+3}{60}=\frac{12}{60}=\frac{1}{5}$

Work done by $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ together in 2 days $=\frac{2}{5}$

Work remaining $=1-\frac{2}{5}=\frac{3}{5}$

Work done by $\mathrm{A}$ and $\mathrm{B}$ in one day $=\frac{1}{15}+\frac{1}{12}=\frac{9}{60}=\frac{3}{20}$

Time required by $\mathrm{A}$ and $\mathrm{B}$ to complete the remaining work together $=\frac{3}{5} \div \frac{3}{20}=\frac{3}{5} \times \frac{20}{3}=4$ days