Question

A and B can do piece of work in 18 days; B and C in 24 days and A and C in 36 days. In what time can they do it, all working together?

Answer 1

A and B's one day work $=\frac{1}{18}$

B and C' one day work $=\frac{1}{24}$

C and A's one day work $=\frac{1}{36}$

$\therefore$ Adding we get:

2(A+B+C)'s one days work $=\frac{1}{18}+\frac{1}{24}+\frac{1}{36}$

$=\frac{4+3+2}{72}=\frac{9}{72}=\frac{1}{8}$

$\therefore$ A+B+C's one day work $=\frac{1}{8}\times \frac{1}{2}=\frac{1}{16}$

$\therefore$ A, B and C can do the whole work in 16 days