‘A’ and ‘B’ can do a piece of work in 20 days and 12 days respectively. ‘A’ started the work alone and then after 4 days ‘B’ joined him till the completion of the work. How long did the work last ?

A's work rate = 1/20 per day. B's rate = 1/12 per day. A works alone for 4 days, completing 4/20 = 1/5 of work. Remaining work = 4/5. Combined rate = 1/20 + 1/12 = 8/120 = 1/15 per day. Time for remaining work = (4/5) / (1/15) = 12 days. Total time = 4 + 12 = 16 days. Wait, this doesn't match any option. Let me reconsider - if A worked for 4 days, then B joined: Combined work in 4 days by A = 4/20 = 1/5. Remaining = 4/5. Combined rate = 1/20 + 1/12 = 2/15. Time = (4/5) / (2/15) = 6 days. Total = 4 + 6 = 10 days. Option C is correct.