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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.
Solution
Let the number of boys be 3x.
Then, number of girls = 2x
3x + 2x = 630
⇒ 5x = 630
⇒ x = 126
⇒ Number of boys = 3x = 3 x 126 = 378
And, Number of girls = 2x = 2 x 126 = 252
After admission of 90 new students, we have
Total number of students = 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 after new admission = 7x = 7 x 60 = 420
And Number of girls after new admission = 5x = 5 x 60 = 300
Number of newly admitted boys = 420 - 378 = 42
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