Question
Quantity 1 : A and B together can paint a wall in 12
hours. A alone can paint it in 18 hours. B paints for 5 hours, and then A completes the remaining work. How many total hours did they take to paint the wall? Quantity 2 : X and Y together can paint a wall in 14 hours. X alone can paint it in 20 hours. Y paints for 8 hours, and then X completes the remaining work. How many total hours did they take to paint the wall?Solution
For Quantity 1 : A’s rate = 1/18, B’s rate = 1/12 - 1/18 = 1/36 Work done by B in 5 hours = 5 × 1/36 = 5/36 Remaining work = 1 - 5/36 = 31/36 Time taken by A to finish remaining work = (31/36) ÷ (1/18) = 15.5 hours Total time = 5 + 15.5 = 20.5 hours Quantity 1 = 20.5 hours For Quantity 2 : X’s rate = 1/20, Y’s rate = 1/14 - 1/20 = 3/140 Work done by Y in 8 hours = 8 × 3/140 = 6/35 Remaining work = 1 - 6/35 = 29/35 Time taken by X to finish remaining work = (29/35) ÷ (1/20) = 16.57 hours Total time = 8 + 16.57 = 24.57 hours Quantity 2 = 25.71 hours Correct option : b) Quantity 1 < Quantity 2
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