Question
Working alone, βXβ and
βYβ can complete a work in 16 days and 10 days, respectively. They started working together but after 4 days, βYβ was replaced by βZβ and the work got finished in the next 4 days. Find the time taken by βZβ alone to finish the whole work.Solution
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 = 13Γ4=52 units. Remaining work = 80β52=28 units.
Efficiency of Z = 7β5=2 units/day.
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