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.
Answer & explanation
Correct answer: option 1
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