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

The correct option is B $24$ days

Solution:-

Let the amount of work done by $A,B,$ and $C$ per day be $x,y$ and $z$ respectively.

Case I:-

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

$\therefore$ work done by $A$ and $B$ in one day $=\frac{1}{12}$

$\Rightarrow x+y=\frac{1}{12}$

Case II:-

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

$\therefore$ work done by B and C in one day $=\frac{1}{16}$

$\Rightarrow y+z=\frac{1}{16}$

As given, A has worked for $5$ days and B has worked for $7$ days, C can finish the rest in $13$ days.

$5x+7y+13z=1$

$\Rightarrow$ $5x+5y+2y+2z+11z=1$

$\Rightarrow$ $5(x+y)+2(y+z)+11z=1$

$\Rightarrow 5\times \frac{1}{12}+2\times \frac{1}{16}+11z=1$

$\Rightarrow 11z=1-\frac{5}{12}-\frac{1}{8}$

$\Rightarrow 11z=\frac{22}{48}$

$\Rightarrow z=\frac{1}{24}$

Therefore, work done by $C$ $1$ day $=\frac{1}{24}$

Hence, C alone can finish the work in $24$ days.