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Question
A school has 630 students. The ratio of the number of boys to the number of girls is 3 : 2. This ratio changes to 7 : 5 after the admission of 90 new students. Find the number of newly admitted boys.
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Solution
Let the number of boys be 3x.
Then, the number of girls = 2x
∴ 3x + 2x = 630
`=>` 5x = 630
`=>` x = 126
`=>` Number of boys = 3x = 3 × 126 = 378
And Number of girls = 2x = 2 × 126 = 252
After admission of 90 new students we have total number of student = 630 + 90 = 720
Now, let the number of boys be 7x
Then, number of girls = 5x
∴ 7x + 5x = 720
`=>` 12x = 720
`=>` x = 60
`=>` Number of boys = 7x = 7 × 60 = 420
And Number of girls = 5x = 5 × 60 = 300
∴ Number of newly admitted boys = 420 – 378 = 42
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