A is 30% more efficient than B. B works for 12 days, and the remaining work is completed by A alone in 20 days. In how many days will B, working alone, to complete half of the total work?

Let B's efficiency = 1 unit/day. Then A's efficiency = 1.3 units/day (30% more). Let total work = W. B works for 12 days: work done = 12 units. Remaining work = W - 12. A completes this in 20 days: 1.3 × 20 = 26 units = W - 12. Therefore W = 38 units. B's rate = 1 unit/day, so B alone takes 38 days for full work. For half the work: 38/2 = 19 days.