‘A’ can do a piece of work in 20 days and ‘B’ can do the same work in 12 days. Find the number of days in which they can complete the whole work if they work on alternate days and the work is started by ‘A’?

A's work per day = 1/20, B's = 1/12. They work alternately starting with A. In 2 days, work done = 1/20 + 1/12 = 8/60 = 2/15. After 14 complete cycles (28 days), work = 28/15 ≈ 1.87 > 1, so fewer cycles needed. After 7 cycles (14 days), work = 14/15. Remaining 1/15 done by A in (1/15)/(1/20) = 4/5 days. Total = 14 + 4/5 = 76/5 days.