Question

A, B and C can do a piece of work in 36, 54 and 72 days respectively. They started the work but A left 8 days before the completion of the work while B left 12 days before completion. The number of days for which C worked is

• A. 4
• B. 8
• C. 12
• D. 24

Answer 1

The correct option is D 24

A does the work in 36 days.

$\therefore$ In 1 day A does $\frac{1}{36}$ work.

B does the work in 54 days.

$\therefore$ In 1 day B does $\frac{1}{54}$ work.

C does the work in 72 days.

$\therefore$ In 1 day C does $\frac{1}{72}$ work.

Let the work is finished in x days.

So A works for x-8 days.

$\therefore$ A does $\frac{x-8}{36}$ work

B works for x-12 days.

$\therefore$ B does $\frac{x-12}{54}$ work.

C works for x days.

$\therefore$ C does $\frac{x}{72}$ work.

The sum of their works = the whole work = 1 work.

$\therefore$ $\frac{x-8}{36}+\frac{x-12}{54}+\frac{x}{72}=1⟹\frac{6x-48+4x-48+3x}{216}=1⟹\frac{13x-96}{216}=1⟹13x=312⟹x=24$

So the work is finished in 24 days.