Question

A and B complete a piece of work in 24 days. B and C do the same work in 36 days; and A, B and C together finish it in 18 days. In how many days will

i) A alone,

ii) C alone,

iii) A and C together, complete the work?

Answer 1

A and B complete a piece of work in = 24 days
B and C complete a piece of work in = 36 days
(A+B+C) complete a piece of work in = 18 days
$\therefore$ (A+B)'s 1 day work $=\frac{1}{24}$
(B+C)'s 1 day work $=\frac{1}{36}$
(A+B+C)'s 1 day work $=\frac{1}{18}$
i) A's 1 day work $=\frac{1}{18}-\frac{1}{36}$
$=\frac{2-1}{36}=\frac{1}{36}$
$\therefore$ A will complete the work in = 36 days.

ii) C's 1 day work $=\frac{1}{18}-\frac{1}{24}$
$=\frac{4-3}{72}=\frac{1}{72}$
$\therefore$ C will complete the work in = 72 days.

iii) (A+C)'s 1 day work $=\frac{1}{36}+\frac{1}{72}$
$=\frac{2+1}{72}=\frac{3}{72}$
$=\frac{1}{24}$
$\therefore$ (A+C) will complete the work in = 24 days.