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.

20 

Let the number of new boys be x, 

               Boys  :  Girls

Original      5     :     3

New          14    :     9

            _______________

             +x            +30

Using cross - multiplication method,

⇒ $\frac{5R+x}{3R+30} = \frac{14}{9}$

45r - 42r = (30 x 14) - (9x)         ----------(i)

Total no. of students originally = 8r = 640  or r = 80

⇒       3r = 420 - 9x

⇒       9x = 420 - 240

⇒        x = 20