A can complete a work in 21 days and B can complete the same work in 16 days. If they work together, in how many days will the work be completed? MCQ with Answer and Explanation

Explanation:
Combined rate = 1/20 + 1/14. Required time = 8.24 days.

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.

Explanation:
Total work = 14 × 12 = 168 man-days. Required days = 168/18 = 9.33 days.