If 'A' needs 24 more days to complete a certain task

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 × (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 × 3x) or, 3x = 5 × (x - 12) or, 3x = 5x - 60 or, 2x = 60 x = 30 So, time taken by 'B' to finish the work alone = 3x = (30 × 3) = 90 days