A alone can complete a work in 12 days and B alone can complete the same work in 18 days. They started working together, but A left after 3 days. In how many days will B alone be able to complete the remaining work?

Correct option is C

Given:

A can complete the work in 12 days.

B can complete the work in 18 days.

A and B worked together for 3 days.

Formula Used:

Rate of Work: If a person takes 'x' days to complete a work, their daily work rate is $$\frac{1}{x}$$​.

Total Work Done: Total Work Done = Time Taken × Rate of Work

Solution:

A's daily work rate: $$\frac{1}{12}$$​​

B's daily work rate: $$\frac{1}{18}$$​​

Combined daily work rate: $$\frac{1}{12}$$​+ $$\frac{1}{18}$$​= $$\frac{5}{36}$$​​

Work done together:$$\frac{5}{36} \times$$​ 3 = $$\frac{5}{12}$$​​

Remaining work: 1 - $$\frac{5}{12}$$​ = $$\frac{7}{12}$$​​

Days for B: $$\frac{\frac{7}{12}}{\frac{1}{18}}$$​=  $$\frac{7}{12} \times$$​18 = $$\frac{21}{2}$$​ = 10.5 days

Therefore, B alone will be able to complete the remaining work in 10.5 days.