Question

A. B and C can do a piece of work in 15, 12 and 20 days respectively. They started the work together. but C left after 2 days. In how many days will the remaining work he completed by A and B?

Answer 1

A's one day's work $=\frac{1}{15}$

B's one day's work $=\frac{1}{12}$

C's one day's work $=\frac{1}{20}$

A,B and C's one day's work

$=\frac{1}{15}+\frac{1}{12}+\frac{1}{20}$

$=\frac{4+5+3}{60}$ (LCM of 15,12,20=60)

$=\frac{12}{60}=\frac{1}{5}$

A,B and C's 2 days work $=\frac{1}{5}\times 2=\frac{2}{5}$

Remaining work $=1-\frac{2}{5}$

$=\frac{5-2}{5}=\frac{3}{5}$ A and B's one days work $=\frac{1}{15}+\frac{1}{12}$

$=\frac{4+5}{60}=\frac{9}{60}=\frac{3}{20}$

$\therefore$ A and B will do the remaining work $\frac{3}{5}in=\frac{20}{3}\times \frac{3}{5}=4$ days