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
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Solution(By Apex Team)
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,
$\begin{array}{l}
=\frac{5}{6} \times 18 \\
=15 \text { days }
\end{array}$
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