Question

$A$ and $B$ together can complete a piece of work in 16 days while $B$ and $C$ together can complete the same work in 12 days and $A$ and $C$ together in 24 days. Find out the number of days that $A$ will take to complete the work, working alone.

• A. 36 days
• B. 48 days
• C. 96 days
• D. 80 days

Answer 1

The correct option is C 96 days

1 day's work of $(A+B)+(B+C)+(C+A)=\frac{1}{16}+\frac{1}{12}+\frac{1}{24}=\frac{9}{48}$
$\Rightarrow$ 1 day's work of $(A+B+C)=\frac{1}{2}\times \frac{9}{48}=\frac{9}{96}$
$\therefore$ 1 day's work of $A$ alone $=\frac{9}{96}-\frac{1}{12}=\frac{1}{96}$
$\therefore A$ can do the whole work alone in $96$ days.