X, Y, and Z alone can complete a language translation in 60, 90, and 36 days respectively. They started working together, but after 5 days, Z left the job, and 20 days before completion, X also left the job. In how many days is the translation completed?

ATQ, Let the total work = 180 units (LCM of 60, 90, and 36) Amount of work done by X alone in one day = 180/60 = 3 units Amount of work done by Y alone in one day = 180/90 = 2 units Amount of work done by Z alone in one day = 180/36 = 5 units Amount of work done by X, Y, and Z together in 5 days = 5 × (3 + 2 + 5) = 50 units Amount of work done by Y alone in 20 days = 20 × 2 = 40 units Remaining work = 180 – 50 – 40 = 90 units Time taken by X and Y together to complete 90 units work = 90/(3 + 2) = 18 days So the total time taken to complete the translation = 5 + 20 + 18 = 43 days