Question
‘A’ is 50% more efficient than ‘B’. ‘A’ and ‘B’ work together for 6 days after which ‘A’ is replaced by ‘C’. ‘B’ and ‘C’ together take 6 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 50% work alone.
Solution
Let the efficiency of 'B' be 'x' units/day So, efficiency of 'A' = x × 1.5 = '1.5x' units/day Total work = 20 × 1.5x = '30x' units So, work done by 'A' and 'B' together in 6 days = (x + 1.5x) × 6 = '15x' units So, remaining work = 30x - 15x = '15x' units So, efficiency of 'B' and 'C' together = 15x ÷ 6 = '2.5x' units per day So, efficiency of 'C' = 2.5x - x = '1.5x' units/day So, required time = (30x × 0.5) ÷ 1.5x = 10 days
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