Question
5 men and 1 boy together can complete a work in 25 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 56% 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 = (5M + B) × 25 = (3M + 5B) × 20 Or, 125M + 25B = 60M + 100B Or, 65M = 75B So, M : B = 15 : 13 Let 'M' = '15x' and 'B' = '13x' Then, total work = (5×15x + 1×13x) × 25 = (75x + 13x) × 25 = '2200x' units 56% of the total work = 2200x × 0.56 = '1232x' units Time taken by 1 man and 1 boy together = 1232x ÷ (15x + 13x) = 1232/28 = 44 days
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