Question

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

• A. $24$ days
• B. $20$ days
• C. $14$ days
• D. $22$ days

Answer 1

The correct option is A $24$ days

(A+B+C)'s 1 day's work $=\frac{1}{18}$

(A+B)'s 1 day's work $=\frac{1}{24}$

(B+C)'s 1 day's work $=\frac{1}{36}$

$\therefore$ (A+C)'s 1 day's work=$(2\times \frac{1}{18})-(\frac{1}{24}+\frac{1}{36})$

$\Rightarrow \left(\frac{1}{9}\right)-\left(\frac{3+2}{72}\right)$

$\Rightarrow (\frac{1}{9}-\frac{5}{72})$

$\Rightarrow \left(\frac{8-5}{72}\right)$

$\Rightarrow \frac{3}{72}=\frac{1}{24}$

so A and C together will do the work in $24$ days.