Question
‘A’ is 40% more efficient than ‘B’. ‘A’ and ‘B’ work together for 8 days after which ‘A’ is replaced by ‘C’. ‘B’ and ‘C’ together take 4 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 × 1.4 = '1.4x' units/day Total work = 20 × 1.4x = '28x' units So, work done by 'A' and 'B' together in 8 days = (x + 1.4x) × 8 = '19.2x' units So, remaining work = 28x - 19.2x = '8.8x' units So, efficiency of 'B' and 'C' together = 8.8x ÷ 4 = '2.2x' units per day So, efficiency of 'C' = 2.2x - x = '1.2x' units/day So, required time = (28x × 0.6) ÷ 1.2x = 14 days
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