X alone can do a piece of work in 6 days and Y alone in 8 days. X and Y undertook to do it for Rs. 4800. With the help of Z, they completed the work in 3 days. How much is to be paid to Z?

The one-day work of X, Y and Z working together is 1/3, as they finish the job in 3 days. Since X alone takes 6 days and Y alone takes 8 days, Z's one-day work is found by subtracting their individual efforts: 1/3 - 1/6 - 1/8. Finding a common denominator of 24 gives 8/24 - 4/24 - 3/24 = 1/24, which means Z's work ratio is 1 out of the total 8 parts of work done per day (4+3+1). Z is therefore paid 1/8 of the total Rs. 4800, which is Rs. 600.

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