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:

A. 10 days

B. 12 days

C. 15 days

D. 16 days

Answer: Option C $\begin{array}{l} (B+C) \text { 2 days work } \\ =2 \times\left(\frac{1}{20}+\frac{1}{30}\right) \\ =2 \times \frac{3+2}{60} \\ =\frac{1}{6} \text { part } \end{array}$ Remaining work $\begin{array}{l} =1-\frac{1}{6} \\ =\frac{5}{6} \text { part } \end{array}$ A’s is one day’s work $=\frac{1}{18} \text { part }$ Time taken to complete the work, $=\frac{\frac{5}{6}}{\frac{1}{18}} \text { days }$ Hence, Time taken to complete the work, $\begin{array}{l} =\frac{5}{6} \times 18 \\ =15 \text { days } \end{array}$