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3 men can do work in = 15 days 4 women can do work in = 20 days 5 boys can do work in = 25 days According to question First 3 days work = (3M + 2W) × 3 Next 3 days work = (2W + 5B) × 3 So total 6 days work = (3M + 4W + 5B) × 3 = (1/15+ 1/20+1/25)× 3 = (1/5+ 3/20+3/25) = (20 + 15 +12 )/100 = 47/100 Remaining work = 1- 47/100 = 53/100 1 day work for 3 men and 5 boys = 1/15+ 1/25 = (10 + 6)/150 = 16/150 So 3 men and 5 boys will take days to complete the remaining work = (53/100) × (150/16) = 4(31/32) days
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