Question

A can do a piece of work in 20 days, while B can do it in 15 days, with the help of C, they finished the work in 5 days. In what time would C alone do it?

Answer 1

$A$ alone do work in $20$ days.

$B$ alone can do work in $15$ days.

$A,B,C$ together can do work in $5$ days.

Lets suppose $C$ alone do work in $x$ days.

$\frac{1}{5}=\frac{1}{25}+\frac{1}{15}+\frac{1}{x}$

$\frac{15-3-5}{75}=\frac{1}{x}$

$\frac{7}{75}=\frac{1}{x},x=\frac{75}{7}$ days

$C$ alone do work in $\frac{75}{4}$ days or $10.71$ days.