Question
If 'A' needs 24 more days to complete a certain task
working alone compared to when 'A' and 'B' work together, and 'A' is 50% more efficient than 'B', what is the amount of time 'B' takes to finish the same task on their own?Solution
Let the time taken by 'A' to finish the work alone be '2x' days. Ratio of efficiencies of 'A' and 'B' = 3:2 Since, the work done is same, ratio of efficiencies of 'A' and 'B' will be inverse of the ratio of time taken by 'A' and 'B' to finish the work. So, time taken by 'B' to finish the work alone = 2x Ă— (3/2) = '3x' days So, time taken by 'A' and 'B' to finish the work together = (2x - 24) days ATQ: (1/2x - 24) = (1/3x) + (1/2x) or, (1/2(x - 12)) = (2x + 3x)/(2x Ă— 3x) or, 3x = 5 Ă— (x - 12) or, 3x = 5x - 60 or, 2x = 60 x = 30 So, time taken by 'B' to finish the work alone = 3x = (30 Ă— 3) = 90 days
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