X can do a piece of work in 40 days. He works at it for 8 days and then Y alone finishes the remaining work in 16 days. How long will X and Y together take to complete the work? MCQ with Answer and Explanation

Explanation:
Combined rate = 1/28 + 1/39. Time = 16.3 days.

Explanation:
Total work = LCM(9, 12) = 36 units. Efficiency of A = 4, B = 3. In 2 days (A + B), work done = 4 + 3 = 7 units. In 10 days (5 pairs of 2 days), work done = 7 * 5 = 35 units. Remaining work = 36 - 35 = 1 unit. On the 11th day, it is A's turn. Time taken by A to complete 1 unit = 1/4 day. Total time = 10 + 1/4 = 10(1/4) days.

Explanation:
Total work = 288 man-days. Time = 288/21 = 13.71 days.