Question

A can finish a work in 36 months, B in 18 months and C in 24 months. B and C start the work but are forced to leave after 4 months. The remaining work was done by A in:

• A. 24 months
• B. 11 months
• C. 22 months
• D. 20 months
• E. None of these

Answer 1

The correct option is C

22 months

(B + C)`s 1 month`s work = $\frac{1}{18}+\frac{1}{24}=\frac{7}{72}$

work done by B and C in 4 months = $\frac{7}{72}\times 4=\frac{7}{18}$

Remaining work = $1-\frac{7}{18}=\frac{11}{18}$

Now, 1/36 work is done by A in 1 month

So, 11/18 work is done by A in $36\times \frac{11}{18}=22$ months