A can complete a work in 17 days and B can complete the same work in 27 days. If they work together, in how many days will the work be completed? MCQ with Answer and Explanation

Explanation:
Total work = LCM(30, 40) = 120 units. Efficiency of A = +4, B = -3. In 2 days, net work = 4 - 3 = 1 unit. We look for when the work reaches 120 - 4 = 116 units. 116 units are done in 116 * 2 = 232 days. On the 233rd day, A works and completes 4 units, making total work 116 + 4 = 120 units. Thus, the wall is completed in 233 days.

Explanation:
Total work = LCM(20, 12) = 60 units. Efficiency of A = 3, B = 5. In 4 days, A alone completes = 4 * 3 = 12 units. Remaining work = 60 - 12 = 48 units. Combined efficiency of A and B = 3 + 5 = 8. Time taken together for remaining work = 48 / 8 = 6 days. Total duration of work = 4 + 6 = 10 days.

Explanation:
Combined rate = 1/13 + 1/28. Time = 1 ÷ combined rate = 8.88 days.