A and B can do job in 10 days and 5 days, respectively. They worked together for two days, after which B was replaced by C and the work was finished in the next three days. How long will C alone take to finish 40% of the job?

12 days

A = 10 days, B = 5 days, 

⇒ A + B worked for 2 days = (1 + 2) x 2 = 6 units.

⇒ Remaining work = 4 units.

⇒ B was replaced by C and the remaining work was completed in 3 days = \(\frac{4}{1 + C}\) = 3 days. 

⇒ 4 = 3 + 3C

⇒ C = \(\frac{1}{3}\) (Efficiency)

⇒ 40% of total work = 40% of 10 = 4 units.

⇒ Time taken by C alone to complete 4 units = \(\frac{4}{1/3}\) = 4 x 3 = 12 days.   ..(\(\frac{Work}{Efficiency}\) = Time)