Working alone, ‘X’ and ‘Y’ can complete a work in 16 days and 10 days, respectively. They started working together but after 4 days, ‘Y’ was replaced by ‘Z’ and the work got finished in the next 4 days. Find the time taken by ‘Z’ alone to finish the whole work.
Let the total work be 80 units (LCM of 16 and 10).
Combined efficiency of X and Y = 5+8=13 units/day. Work done by X and Y together in 4 days = 13×4=52 units. Remaining work = 80−52=28 units. 
Efficiency of Z = 7−5=2 units/day.
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