Question
Calculate the number of days it would take for a team of
8 boys, 5 girls, and 5 children to Construct a building. This building was previously constructed by a team of 18 boys and 12 girls in 12 days, and later by 74 boys and 30 girls in 3 days. Additionally, note that each girl's efficiency is 50% less than that of each child.Solution
We can say that Let the efficiency of each boy and each girl be 'B' units/day and 'G' units/day, respectively. So, efficiency of a child = (G/0.50) = '2G' units per day According to the question, (18B + 12G) Ă— 12 = (74B + 30G) Ă— 3 Or, 216B + 144G = 222B + 90G Or, 6B = 54G Or, B = 9G Therefore, Total work = (18B + 12G) Ă— 12 = (9 Ă— 18G + 12G) Ă— 12 = '2088G' units Combined efficiency of 8 boy, 5 Girl and 5 children = (8 Ă— 9G) + 5G + (5 Ă— 2G) = 72G + 5G + 10G = '87G' units per day Required time taken = (2088G/87G) = 24 days.
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