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    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.
    A 1350 Correct Answer Incorrect Answer
    B 1050 Correct Answer Incorrect Answer
    C 900 Correct Answer Incorrect Answer
    D 1200 Correct Answer Incorrect Answer
    E 1500 Correct Answer Incorrect Answer

    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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