Question
‘A’ is 25% more efficient than ‘B’. ‘A’ and ‘B’ work together for 5 days after which ‘A’ is replaced by ‘C’. ‘B’ and ‘C’ together take 5 more days to finish the work. If ‘A’ alone could’ve finished the whole work in 16 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 × 1.25 = '1.25x' units/day Total work = 16 × 1.25x = '20x' units So, work done by 'A' and 'B' together in 5 days = (x + 1.25x) × 5 = '11.25x' units So, remaining work = 20x - 11.25x = '8.75x' units So, efficiency of 'B' and 'C' together = 8.75x ÷ 5 = '1.75x' units per day So, efficiency of 'C' = 1.75x - x = '0.75x' units/day So, required time = (20x × 0.6) ÷ 0.75x = 16 days
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