Question
6 men and 2 boys together can complete a work in 15 days. 3 men and 5 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 50% 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 5 boys together to complete the entire work = 10 × 2 = 20 days Then, total work = (6M + 2B) × 15 = (3M + 5B) × 20 Or, 90M + 30B = 60M + 100B Or, 30M = 70B So, M : B = 7 : 3 Let 'M' = 7x and 'B' = 3x Then, total work = (7x × 6 + 3x × 2) × 15 = (42x + 6x) × 15 = 48x × 15 = 720x units 50% of the total work = 720x × 0.5 = 360x units Time taken by 1 man and 1 boy together to complete 50% of the work = 360x ÷ (7x + 3x) = 360 ÷ 10 = 36 days
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