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 forced to leave after $3$ days. The remaining work was done by $A$ in:

• A. $25$ days
  
• B. $10$ days
  
• C. $16$ days
  
• D. $31$ days
  

Answer 1

The correct option is B $10$ days

Work done by $A$ in one day $=\frac{1}{24}$

Work done by $B$ in one day $=\frac{1}{9}$

Work done by $C$ in one day $=\frac{1}{12}$

Work done by $B$ and $C$ in 3 days $=3(\frac{1}{9}+\frac{1}{12})=\frac{21}{36}$

Time taken by $A$ to finish remaining ${\frac{15}{36}}^{th}$ work $=\frac{15}{36}\times 24$ $=10$ days