A can do a piece of work in 90 days, B can do it in 40 days and C can do in 12 days. They take turns and work for a day each, i.e. on the first day, A works alone; on the second day, B works alone; and on the third day, C works alone. The cycle is repeated till the work is finished. They get $240 for this job. If the wages are divided in proportion to the work each has done, then find the amounts each will get.

The total work is the least common multiple of 90, 40, and 12, which is 360 units. Their daily outputs are 4 units for A, 9 units for B, and 30 units for C. After A, B, and C work sequentially for three days, they complete 43 units, meaning eight full cycles account for 344 units. On the 25th day, A completes 4 units and B completes the remaining 12 units, making their total individual outputs 36 units for A, 84 units for B, and 240 units for C. Wages are distributed in this proportion, so A receives 36 divided by 360 of 240 dollars, which is 24 dollars, B receives 54 dollars, and C receives 162 dollars.

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