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Let the efficiency of 'X' and 'Y' be 'x' units/day and 'y' units/day, respectively. ATQ; 36 × (x + y) = 20 × (x + y) + 40y Or, 36x + 36y = 20x + 60y Or, 16x = 24y So, x = (3y/2) So, total work = 36 × {(3y/2) + y} = 36 × (5y/2) = '90y' units So, required time = 90y ÷ y = 90 days Alternate Solution Part of the work completed by 'X' and 'Y' together in 20 days = (20/36) = (5/9) Remaining part of the work = 1 - (5/9) = (4/9) which is completed by 'Y' alone in 40 days Therefore, time taken by 'Y' to complete the whole work alone = 40 ÷ (4/9) = 40 × (9/4) = 90 days
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