Question
3 men and 1 boy together can complete a work in 20 days.
2 men and 3 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 60% 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 3 boys together to complete the entire work = 10 × 2 = 20 days Then, total work = (3M + B) × 20 = (2M + 3B) × 20 Or, 3M + B = 2M + 3B Or, M = 2B So, M : B = 2 : 1 Let 'M' = 2x and 'B' = x Then, total work = (2x × 3 + x) × 20 = 7x × 20 = 140x units 60% of the total work = 140x × 0.6 = 84x units Time taken by 1 man and 1 boy together to complete 60% of the work = 84x ÷ (2x + x) = 84 ÷ 3 = 28 days
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