A can complete a piece of work in 16 days and B in 12 days. Starting with A, they work on alternate days. In how many days will the total work be completed? MCQ with Answer and Explanation

Total work = LCM(16, 12) = 48 units. Efficiency of A = 3, B = 4. In a 2-day cycle (A then B), work completed = 3 + 4 = 7 units. In 6 cycles (12 days), work completed = 7 * 6 = 42 units. Remaining work = 48 - 42 = 6 units. On Day 13, A works and completes 3 units. Remaining work = 3 units. On Day 14, B works with efficiency 4, so time taken = 3/4 day. Total time = 12 + 1 + 3/4 = 13(3/4) days.