Question

The ratio of the number of boys to the number of girls in a school of 560 pupils is 5 : 3. If 10 new boys are admitted, find how many new girls may be admitted so that the ratio of the number of boys to the number of girls may change to 3 : 2.

Answer 1

Ratio between boys and girls = 5 : 3

No. of pupils = 560

Sum of ratios = 5 + 3 = 8

∴ No of boys = `(5)/(8) xx 560` = 350

and No of girls = `(3)/(8) xx 560` = 210

No. of new boys admitted = 10

∴ Total number of boys = 350 + 10 = 360

Let the no. of girl admitted = x

∴ Total number of girls = 210 + x

Now according to the condition,

360 : 210 + x = 3 : 2

⇒ `(360)/(210 + x) = (3)/(2)`

⇒ 630 + 3x = 720

⇒ 3x = 720 – 630

⇒ 3x = 90

⇒ x = `(90)/(3)`

⇒ x = 30

∴ No of girls to be admitted = 30.