Question

in a group of 36 students boys and girls are in the ratio of 3:1 respectively how many more girls should be a should be included in the group so that the ratio becomes 9 : 5 respectively

Answer 1

Let the number of boys and girls be
x and y.

Given:
x:y = 3:1
x = 3k and y = k

As per given data,
x + y = 36
3k+k = 36
4k = 36
k = 9.

So there are 27 boys and 9 girls in the group.

Suppose m number of girls are added to group

Then their ratio becomes 9: 5

i. e 27/ (9+m) = 9/5

135= 81 + 9m

54 = 9m

m = 6

Therefore 6 girls should be added to group.

Answer 2

Let the number of the boys and the girls be 3x and x respectively.

∵ No. of girls + No. of Boys = 36
∴ x + 3x = 36
⇒ 4x = 36
⇒ x = 9

Number of the Girls = x = 9 girls..
Number of boys = 3x = 3 × 9
 = 27 boys.

Let the numbers of the girls to be included in the groups be y.

∴ New numbers of the girls = 9 + y

According to the Question,
 No. of boys/New number of girls = 9/5
∴ 27/(9 + y) = 9/5
⇒ 3/(9 + y) = 1/5
⇒ 15 = 9 + y
∴ y = 15 - 9
∴ y = 6


Hence, the number of the girls to be included so that the ratio of the number of boys and the girls will become 5:9 is 6. 


Hope it helps.