Question
X and Y alone can complete a work in 10 and 40 days,
respectively. 50% of the work is completed by Z in 20t days, and the remaining work is completed by X and Y working together in ‘t’ days. Find the time taken by Y and Z to complete the whole work while working together.Solution
Time taken by X and Y to complete the whole work while working together = (10 × 40)/(10 + 40) = 8 days So, t = 8/2 = 4 (Since, 50% of the work is done by X and Y together) As, time taken by Z to complete 50% of the work = 4 × 20 = 80 days So, time taken by Z to complete the entire work = 80 × 2 = 160 days Therefore, time taken by Y and Z to complete the whole work while working together = (160 × 40)/(160 + 40) = 32 days
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