Two teachers A and B can complete an academic work in 10 days and 15 days respectively. They started the work together, but A left after 5 days and another teacher C joined, who alone can complete the work in 60 days. In how many days the work got completed?

A/c to question , A can complete work in 10 days, B in 15 days and C in 60 days.

A and B work together for  days and complete 

5 $$\times (\frac{1}{10} + \frac{1}{15}) = \frac{5}{6}$$ of work

Remaining work = $$\frac{1}{6}$$th of work

B and C together can complete the work in $$(\frac{1}{15} + \frac{1}{60}) = \frac{1}{12}$$

They will complete  $$\frac{1}{6}$$th of work in $$\frac{\frac{1}{6}}{\frac{1}{12}}$$ = 2 days

Total days to complete the work = 5 + 2 = 7 days

So, the answer would be option a)7