Question
‘A’ is 80% more efficient than ‘B’. ‘A’ and ‘B’ work together for 5 days after which ‘A’ is replaced by ‘C’. ‘B’ and ‘C’ together take 10 more days to finish the work. If ‘A’ alone could’ve finished the whole work in 20 days, then find the time taken by ‘C’ to finish 60% work alone.
Solution
Let the efficiency of 'B' be 'x' units/day So, efficiency of 'A' = x × 1.8 = '1.8x' units/day Total work = 20 × 1.8x = '36x' units So, work done by 'A' and 'B' together in 5 days = (x + 1.8x) × 5 = '14x' units So, remaining work = 36x - 14x = '22x' units So, efficiency of 'B' and 'C' together = 22x ÷ 10 = '2.2x' units per day So, efficiency of 'C' = 2.2x - x = '1.2x' units/day So, required time = (36x × 0.6) ÷ 1.2x = 18 days
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