Question

$A$ takes twice as much time as $B$ or thrice as much time as $C$ to finish a piece of work. Working together, they can finish the work in $2$ days. $B$ can do the work alone in

• A. $3$ days
  
• B. $7$ days
  
• C. $4$ days
  
• D. $6$ days
  

Answer 1

The correct option is D $6$ days

Suppose $A,B$ and $C$ take $x,\frac{x}{2}$ and $\frac{x}{3}$ days respectively to finish the work.
Then, $(\frac{1}{x}+\frac{2}{x}+\frac{3}{x})$$=\frac{1}{2}$
$\therefore \frac{6}{x}=\frac{1}{2}$
$\therefore x=12$
So, $B$ takes $\frac{12}{2}=6$ days to finish the work.