A can lay railway track between two given stations in 20 days and B can do the same job in 12 days. With the help of C, they did the job in 2 days only. Then, C alone can do the job in​

Correct option is D

Given:

A can do the work in 20 days.

B can do the work in 12 days.

A, B, and C together complete the work in 2 days.

Find the time taken by C alone.

Solution:

Efficiency of (A+B) = $$\frac{1}{20} + \frac{1}{12}$$​​

​$$= \frac{3+5}{60} = \frac{8}{60} = \frac{2}{15}$$​​

Efficiency of (A+B+C) = $$\frac{1}{2}$$​​

Efficiency of C = $$\frac{1}{2} - \frac{2}{15}$$​​

​$$= \frac{15-4}{30} = \frac{11}{30}$$​​

Time taken by C alone = $$\frac{30}{11}$$ = $$2\frac{8}{11}$$​ days

Alternate Solution(Exam based):