A has completed two-third of a job in 8 days, and B completes the rest of the job in 20 days. In how many days can they together complete the job?

Correct option is C

Given:

A can two-third of work in 8 days

B can do rest of work same work in 20 days

Formula Used:

Let total work be 1.

Then work done 1 day =$$\frac{1}{Total\ time\ to\ work}$$​ 

Solution:

A can do two-third of work in 8 days

So A can do the whole work in $$8\times \frac{3}{2}$$​ = 12days

Rest of the work = $$1-\frac{2}{3} = \frac{1}{3}$$​​

Then B can do $$\frac{1}{3}$$​rd  of the work in 20 days

B can do whole work = $$20 \times 3$$​ = 60days

A’s one day’s work = $$\frac{1}{12}$$​​

B’s one day’s work =$$\frac{1}{60}$$​​

A and B’s one day work together = $$\frac{1}{12}+\frac{1}{60}$$​​

​$$= \frac{5+1}{60}=\frac{1}{10}$$​​

Time taken by A and B to complete the work  =$$\frac{1}{\frac{1}{10}} = 10days$$​​