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.

Medium

Solution

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Let’s consider the number of boys be 3x
Then, the number of girls = 2x
3x + 2x = 630
5x = 630
x = 126
So, the number of boys = 3x = 3 126 = 378
And, number of girls = 2x = 2 126 = 252
After admission of 90 new students
Total number of students = 630 + 90 = 720
Here, let take the number of boys to be 7x
And, the number of girls = 5x
7x + 5x = 720
12x = 720
x = 720/12
x = 60
So, the number of boys = 7x = 7 60 = 420
And, the number of girls = 5x = 5 60 = 300
Therefore, the number of newly admitted boys = 420 – 378 = 42

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