Question

$A$ can finish a work in $24$ days, $B$ in $9$ days and $C$ in $12$ days. $B$ and $C$ start the work but are force to leave after $3$ days. The remaining work was done by $A$ in:

• A. $5$ days
• B. $6$ days
• C. $10$ days
• D. $10\frac{1}{2}$ days

Answer 1

Answer: (C)

$10$ days

$(B+C)$'s $1$ day's work $=(\frac{1}{9}+\frac{1}{12})=\frac{7}{36}$
Work done by $B$ and $C$ in $3$ days $=(\frac{7}{36}\times 3)=\frac{7}{12}$
Remaining work $=(1-\frac{7}{12})=\frac{5}{12}$
Now, $\frac{1}{24}$ work is done by $A$ in $1$ day.
So, $\frac{5}{12}$ work done by $A$ in $(24\times \frac{5}{12})=10$ days.