Question

$A$ and $B$ can do a piece of work in $8$ days. $B$ and $C$ can do the same work in $12$ days. If $A,B$ and $C$ can complete the same work in $6$ days, in how many days can $A$ and $C$ complete the same work?

• A. $8$ days
• B. $10$ days
• C. $6$ days
• D. $2$ days

Answer 1

The correct option is A $8$ days

$(A+B+C)$'s one days' work $=\frac{1}{6};(A+B)$'s one days' work $=\frac{1}{8};$
$(B+C)$'s one days' work $=\frac{1}{12}$
$\Rightarrow C$'s one days' work $=\frac{1}{6}-\frac{1}{8}=\frac{4-3}{24}=\frac{1}{24}$
Similarly, $A$'s one days' work $=\frac{1}{6}-\frac{1}{12}=\frac{2-1}{12}=\frac{1}{12}$
$\therefore (A+C)$'s one days' work $=\frac{1}{24}+\frac{1}{12}=\frac{1+2}{24}=\frac{3}{24}=\frac{1}{8}$
$\therefore (A+C)$ can finish the work in $8$ days.