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?

7

A = 10 days, B = 15 days,

⇒ A + B worked for 5 days = (3+2) x 5 = 25 units,

⇒ Remaining work = 30 - 25 = 5 units,

⇒ C alone can complete the total work in 60 days = \(\frac{30}{C}\) = 60 days,

⇒ C = \(\frac{1}{2}\)  (Efficiency)

⇒ A left the work and C joins B to complete the remaining work in = \(\frac{5}{5/2}\) = 2 days.    ..(\(\frac{Work}{Efficiency}\) = Time)

Therefore, total time to complete the work is 5 + 2 = 7 days.