Question
In 2022, the ratio of boys to girls in a school was 8:7.
By 2023, 50 boys and 80 girls had left the school, while 90 new boys and 30 new girls joined. As a result, the ratio of girls to boys in the school changed to 3:4. Determine the total number of boys and girls in the school in 2022.Solution
Let the number of boys and girls in the school in 2022 be '8m' and '7m', respectively. ATQ: (8m - 50 + 90) :(7m - 80 + 30) = 4:3 Or, (8m + 40) ÷ (7m - 50) = (4/3) Or, 3 X (8m + 40) = 4 X (7m - 50) Or, 24m + 120 = 28m - 200 Or, 4m = 320 So, 'm' = 80 Therefore, sum of number of boys and girls in the school in 2022: = 8m + 7m = '15m' = 15 X 80 = 1,200
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