Question
In a class of 55 students, the ratio of boys to girls is
5:6. The average weight of a boy exceeds the average weight of a girl by 8 kg. Additionally, the ratio of the total weight of all the boys to that of all the girls is 15:14. Determine the average weight of a boy in the class.Solution
Number of boys in the class = 55 X (5/11) = 25 Number of girls in the class = 55 - 25 = 30 Let the average weight of a girl in the class = 'y' kg Then, average weight of a boy in the class = (y + 8) kg Total weight of all girls in the class = 30 X y = '30y' kg Total weight of all boys in the class = 25 X (y + 8) = (25y + 200) kg According to the question, (25y + 200):(30y) = 15:14 Or, 350y + 2800 = 450y So, y = 2800 ÷ 100 = 28 Therefore, average weight of a boy in the class = 28 + 8 = 36 kg
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