Question

$A$ and $B$ can do a work in $8$ days, $B$ and $C$ can do the same work in $12$ days. $A,B$ and $C$ together can finish it in $6$ days. $A$ and $C$ together will do it in:

• A. $4$ days
• B. $6$ days
• C. $8$ days
• D. $12$ days

Answer 1

The correct option is C $8$ days

$(A+B+C)$'s $1$ day's work $=\frac{1}{6}$;
$(A+B)$'s $1$ day's work $=\frac{1}{8}$;
$(B+C)$'s $1$ day's work $=\frac{1}{12}$;
$\therefore$ $(A+C)$'s $1$ day's work $=(2\times \frac{1}{6})-(\frac{1}{8}+\frac{1}{12})$
$=(\frac{1}{3}-\frac{5}{24})=\frac{3}{24}=\frac{1}{8}$.
So, $A$ and $C$ together will do the work in $8$ days.