Question

When $A,B,C$ are work together they complete the work in $7$ days. When $A$ and $C$ decided to do the work they complete the job in $12$ days. In how many days $B$ alone can complete the work ?

• A. $24$
• B. $21$
• C. $42$
• D. $12$

Answer 1

Answer: (A)

$24$

$A,B$ and $C$ can complete the whole work in $8$.
$A+B+C=8$ days..............(1)
Work rate of $A+B+C=\frac{100}{8}=12.5\%$ per day.
$A$ and $C$ complete the work in $12$ days.
$A+C=12$ days...........(2)
Work rate of $(A+C)=\frac{100}{12}=8.33\%$ per day.
Work rate of $B$ $=(A+B+C)-(A+C)$
$=12.5-8.33=4.16\%$ per day
Therefore, $B$ can complete the entire work alone,
$=\frac{100}{4.16}=24$days.