Question

$A$ can do a piece of work in $120$ days and $B$ can do it in $150$ days. They work together for $20$ days. then, $B$ and $A$ alone continues the work. $12$ days after that $C$ joins $A$ are work is completed in $48$ days more. In how many days can $C$ do it. if he works alone?

• A. $240days$
• B. $200days$
• C. $300days$
• D. $250days$

Answer 1

Answer: (A)

$240days$

Let C completes the work in $d$ days,

$\Rightarrow 20(\frac{1}{120}+\frac{1}{150})+12\times \frac{1}{120}+48(\frac{1}{120}+\frac{1}{d})=1$

$\Rightarrow \frac{2}{5}+\frac{2}{5}+\frac{48}{d}=1$

$\Rightarrow \frac{48}{d}=\frac{1}{5}$

$\Rightarrow d=240days.$