Question

$A$ can complete a piece of work in $18$ days, $B$ in $20$ days and $C$ in $30$ days. If $B$ and $C$ together start the work and are forced to leave after $2$ days, then number of days taken by $A$ alone to complete the remaining work is

• A. $10$
• B. $12$
• C. $15$
• D. $16$

Answer 1

The correct option is C $15$

Two day's work of $(B+C)=2\times (\frac{1}{20}+\frac{1}{30})=\frac{1}{6}$
Remaining work $=1-\frac{1}{6}=\frac{5}{6}$
One day's work of $A=\frac{1}{18}$
Hence, number of days taken to complete the work $=\frac{5/6}{1/18}=15$