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 forced to leave after 2 days. The time taken by A alone to complete the remaining work is:

Solution(By Examveda Team)

1^st Method:
$$\eqalign{ & \left( {B + C} \right)\,2\,{\text{days}}\,{\text{work}} \cr & = 2 \times \left( {\frac{1}{{20}} + \frac{1}{{30}}} \right) \cr & = 2 \times {\frac{{3 + 2}}{{60}}} \cr & = \frac{1}{6}{\text{part}} \cr & {\text{Remaining}}\,{\text{work}} \cr & = 1 - \frac{1}{6} \cr & = \frac{5}{6}\text{part} \cr & {\text{A's}}\,{\text{one}}\,{\text{day's}}\,{\text{work}} \cr & = \frac{1}{{18}}{\text{part}} \cr & {\text{Time taken to complete the work}} \cr & = \frac{{ {\frac{5}{6}} }}{{ {\frac{1}{{18}}} }}\,{\text{days}} \cr & {\text{Hence,}} \cr & {\text{Time taken to complete the work}} \cr & = {\frac{5}{6}} \times 18 \cr & = 15\,{\text{days}} \cr} $$

2^nd Method:
% of work B completes in one day = $$\frac{{100}}{{20}}$$ = 5%;
% of work C completes in one day = $$\frac{{100}}{{30}}$$ = 3.33%;
% of work (A + B) completes together in one day = 5 + 3.33 = 8.33%;
% work (A + B) completes together in 2 days = 8.66 × 2 = 16.66%;
Remaining work = 100 - 16.66 = 83.34%;
% of work A completes in 1 day = $$\frac{{100}}{{18}}$$ = 5.55%
Time taken to complete the remaining work by A
= $$\frac{{83.34}}{{5.55}}$$
= 15 days