Question
Two quantities are
given as Quantity I and Quantity II. You have to determine the relationship between them and give the answer. The efficiencies of a man and a boy are in the ratio 7 : 4. For a building project, 2 men and 3 boys together can finish the job in 12 days. Quantity I: In how many days will 3 men and 2 boys complete the entire job? Quantity II: If the man’s efficiency increases by 20% and the boy’s by 10%, how many days will one man and one boy take to finish 75% of the same job?Solution
ATQ, Let efficiencies be 7x (man) and 4x (boy). Total work = (27x + 34x) * 12 = (14x + 12x) * 12 = 26x * 12 = 312x From Quantity I, Efficiency of 3 men and 2 boys = 37x + 24x = 21x + 8x = 29x Required time = 312x / 29x = 312/29 = ~10.76 days From Quantity II, New man efficiency = 7x * 120/100 = 8.4x New boy efficiency = 4x * 110/100 = 4.4x Total = 8.4x + 4.4x = 12.8x Work to be done = 312x * 75/100 = 234x Required time = 234x / 12.8x = ~18.28 days Thus, Quantity I < Quantity II
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