**Question:**

A and B can do a piece of work in 15 days; B and C in 12 days; C and A in 20 days. How many days will be taken by A, B and C working together to finish the work?

**Solution:**

$(\mathrm{A}+\mathrm{B})$ can do a work in 15 days.

$\therefore(\mathrm{A}+\mathrm{B})$ 's 1 day work $=\frac{1}{15}$

$(\mathrm{B}+\mathrm{C})$ can do a work in 12 days.

$\therefore(\mathrm{B}+\mathrm{C})$ 's 1 day work $=\frac{1}{12}$

$(\mathrm{C}+\mathrm{A})$ can do a work in 20 days.

$\therefore(\mathrm{C}+\mathrm{A})$ 's 1 day work $=\frac{1}{20}$

$2(\mathrm{~A}+\mathrm{B}+\mathrm{C})$ 's 1 day work $=\frac{1}{15}+\frac{1}{12}+\frac{1}{20}=\frac{4+5+3}{60}=\frac{12}{60}=\frac{1}{5}$

$(\mathrm{A}+\mathrm{B}+\mathrm{C})$ 's 1 day work $=\frac{1}{10}$

A, B and C working together require 10 days to complete the work.