Question

A can do a piece of work in 10 days; B in 18 days; and A, B and C together in 4 days. In what time would C alone do it?

Answer 1

A can do a piece of work in = 10 days
B can do a piece of work in = 18 days
(A+B+C) can do a piece of work in = 4 days
$\therefore$ A's 1 day work $=\frac{1}{10}$
B's 1 day work $=\frac{1}{18}$
(A + B)'s 1 day work $=\frac{1}{10}+\frac{1}{18}=\frac{9+5}{90}$
$=\frac{14}{90}=\frac{7}{45}$
(A+B+C)'s 1 day work $=\frac{1}{4}$
$\therefore$ C's 1 day work $=\frac{1}{4}-\frac{7}{45}$
$=\frac{45-28}{180}=\frac{17}{180}$
$\therefore$ C can do the piece of work in $=\frac{180}{17}$ days
$=10\frac{10}{17}$ days.