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.

Answer 1

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