A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how many days will A and B together complete the work? MCQ with Answer and Explanation

A's 10-day work = 10/80 = 1/8. Remaining work = 7/8. B completes 7/8 work in 42 days, so B completes full work in 42 * (8/7) = 48 days. Combined 1-day work = 1/80 + 1/48 = (3 + 5)/240 = 8/240 = 1/30. They finish together in 30 days.