Question
5 men and 3 boys together can complete a work in 16 days. 3 men and 7 boys can together complete half of the same work in 8 days. Find the time taken by 1 man and 1 boy together to complete 75% 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 3 men and 7 boys together to complete the entire work = 8 × 2 = 16 days Then, total work = (5M + 3B) × 16 = (3M + 7B) × 16 Or, 5M + 3B = 3M + 7B Or, 2M = 4B So, M : B = 2 : 1 Let 'M' = 2x and 'B' = x Then, total work = (2x × 5 + x × 3) × 16 = (10x + 3x) × 16 = 13x × 16 = 208x units 75% of the total work = 208x × 0.75 = 156x units Time taken by 1 man and 1 boy together to complete 75% of the work = 156x ÷ (2x + x) = 156 ÷ 3 = 52 days
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