Question
In a class, the ratio of boys to girls is 5:3. If 4 boys
and 2 girls leave the class, the ratio of boys to girls becomes 3:2. How many students were there in the class initially?Solution
Let the number of boys be 5x and the number of girls be 3x. Total students = 5x + 3x = 8x. After 4 boys and 2 girls leave: Boys = 5x - 4, Girls = 3x - 2. The new ratio of boys to girls is given as 3:2: (5x - 4) / (3x - 2) = 3 / 2. 2(5x - 4) = 3(3x - 2) 10x - 8 = 9x - 6 10x - 9x = 8 - 6 x = 2. Substituting x back to find the number of boys and girls: Number of boys = 5x = 5(2) = 10. Number of girls = 3x = 3(2) = 6. Total students = 10 + 6 = 16. Ans. b
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