The ratio of the number of boys to the number of girls in a school of 640 students, is 5 : 3. If 30 more girls are admitted in the school, then how many more boys should be admitted so that the ratio of boys to that of the girls, becomes 14 : 9.

Total student = 640

Ratio boys to girls = 5 : 3

Number of boys = 640 $$\times \frac{5}{8} = 400

Number of girls = 640 - 400 = 240

Now,

Number of girls = 240 + 30 = 270 

Let the new admitted boys be x.

So,

number of boys = 400 + x

ratio of boys to that of the girls = 14 : 9

$$\frac{400 + x}{270} = \frac{14}{9}$$

(400 + x)$$\times 9 = (270) \times 14$$

3600 + 9x = 3780

x = 180/9 = 20

$$\therefore$$ 20 boys should be admitted.