Question
3 men and 2 boys together can complete a work in 30
days. 2 men and 6 boys can together complete half of the same work in 10 days. Find the time taken by 1 man and 1 boy together to complete 55% of the entire work.Solution
Let the efficiency of man and that of a boy be 'M' units/day and 'B' units/day respectively. Time taken by 2 men and 6 boys together to complete the entire work = 10 × 2 = 20 days Then, total work = (3M + 2B) × 30 = (2M + 6B) × 20 Or, 90M + 60B = 40M + 120B Or, 50M = 60B So, M : B = 6 : 5 Let 'M' = '6x' and 'B' = '5x' Then, total work = (3×6x + 2×5x) × 30 = (18x + 10x) × 30 = '840x' units 55% of the total work = 840x × 0.55 = '462x' units Time taken by 1 man and 1 boy together = 462x ÷ (6x + 5x) = 462/11 = 42 days
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