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

Solution(By Examveda Team)

$$\eqalign{ & \left( {{\text{B}} + {\text{C}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{1}{{20}} + \frac{1}{{30}}} \right) \cr & = \frac{5}{{60}} \cr & = \frac{1}{{12}} \cr & \left( {{\text{B}} + {\text{C}}} \right){\text{'s 2 day's work}} \cr & = \left( {\frac{1}{{12}} \times 2} \right) \cr & = \frac{1}{6} \cr & {\text{Remaining work }} \cr & = \left( {1 - \frac{1}{6}} \right) \cr & = \frac{5}{6}{\text{ }} \cr & \left( {{\text{A}} + {\text{B}}} \right){\text{'s 1 day's work}} \cr & = \left( {\frac{1}{{12}} + \frac{1}{{15}}} \right) \cr & = \frac{9}{{60}} \cr & = \frac{3}{{20}} \cr} $$
Now, $$\frac{1}{{18}}$$ work is done by A in 1 day
$$\eqalign{ & \therefore \frac{5}{6}{\text{ work is done by A in }} \cr & = \left( {18 \times \frac{5}{6}} \right) \cr & = 15{\text{ days}} \cr} $$