Question

A and B can do a job in $12$ days, B and C can do it in $16$ days. After A has worked for $5$ days and B has worked for $7$ days, C can finish the rest in $13$ days. In how many days, can C do the work alone?

• A. $16$ days
• B. $24$ days
• C. $36$ days
• D. $48$ days

Answer 1

Answer: (B)

$24$ days

$A$ and $B$ can do a job in $12$ days.

$B$ and $C$ can do a job in $16$ days.

$A$ worked for $5$ days and $B$ worked for $7$ days.

Part of work done by $A$ and $B$ in $5$ days=$\frac{5}{12}$

$\therefore$ Part of work left after $A$ left=$1-\frac{5}{12}=\frac{12-5}{12}=\frac{7}{12}$

After $A$ left work $B$ worked for $2$ more days.

Part of work done by $B$ and $C$ in $2$ days=$\frac{2}{16}=\frac{1}{8}$

$\therefore$ part of work left after $B$ left=$\frac{7}{12}-\frac{1}{8}=\frac{14-3}{24}=\frac{11}{24}$

Now $\frac{11}{24}$ part o work $C$ has to complete in $11$ days

Since $C$ already had worked for $2$ dayswith $B$

(part)complete work is done by $C$ in $\frac{11}{\frac{11}{24}}$

=$24$days.