# A and B can do a piece of work in 18 days; B and C can do it in 24 days while C and A can finish it in 36 days.

**Question:**

A and B can do a piece of work in 18 days; B and C can do it in 24 days while C and A can finish it in 36 days. In how many days can A, B, C finish it, if they all work together?

**Solution:**

Time needed by $\mathrm{A}$ and $\mathrm{B}$ to finish the work $=18$ days

Time needed by $\mathrm{B}$ and $\mathrm{C}$ to finish the work $=24$ days

Time needed by $\mathrm{C}$ and $\mathrm{A}$ to finish the work $=36$ days

Work done by $\mathrm{A}$ and $\mathrm{B}$ in one day $=\frac{1}{18}$

Work done by $\mathrm{B}$ and $\mathrm{C}$ in one day $=\frac{1}{24}$

Work done by $\mathrm{C}$ and $\mathrm{A}$ in one day $=\frac{1}{36}$

$2 \times$ Work done by $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ in one day $=\frac{1}{18}+\frac{1}{24}+\frac{1}{36}=\frac{4+3+2}{72}=\frac{9}{72}=\frac{1}{8}$

$\therefore$ Work done by $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ in one day $=\frac{1}{16}$

So, $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ working together will t ake 16 days to complete the work.