Question

The ratio of boys to girls is 20:11 if 50 more girls were needed to make this ratio 5:4 what was the number of boys in school

Answer 1

Step-by-step explanation:

$\bf Given:-$

• The ratio of boys to girls = 20 : 11

• If 50 more girls are added the ratio becomes 5 : 4

$\bf To\:Find:-$

• The number of boys in the school.

$\bf Solution:-$

Let the number of boys be 20x

The number of girls = 11x

50 girls are added

Number of girls = 11x + 50

If 50 girls are added the ratio becomes 5:4

So:-

$\longrightarrow \sf\dfrac{20x}{11x + 50} = \dfrac{5}{4}$

By cross multiplication:-

$\longrightarrow \sf{4(20x)} = {5(11x + 50)}$

$\longrightarrow \sf{80x} = {55x + 250}$

$\longrightarrow \sf{80x} - {55x = 250}$

$\longrightarrow \sf{25x} = 250$

$\longrightarrow \sf x = \dfrac{250}{25}$

$\longrightarrow \sf x = 10$

Therefore:-

Number of boys = 20x = 20 × 10 = 200

$\boxed{\longrightarrow \bf Number \: of \: boys = 200}$

Answer 2

AnswEr:-

Your Answer Is 200 boys.

ExplanaTion:-

Given:-

• Ratio of boys : Girl = 20 : 11.

• 50 more girls are needed to make this ratio 5 : 4.

To Find:-

• The number of boys in the school.

So,

Since the rato of boys : girl is 20 : 11 therefore let the number of boys and girls in the school be 20x and 11x respectively.

And ATQ:-

↦ Number of Boys : Number of girls + 50 = 5:4.

↦ 20x : (11x + 50) = 5 : 4.

↦ 20x/11x + 50 = 5/4.

↦ 4 (20x) = 5 (11x + 50).

[By cross multiplication].

↦ 80x = 55x + 250.

↦ 80x - 55x = 250.

↦ 25x = 250.

↦ x = 250/25.

↦ x = 10.

So total number of boys in the school,

= 20x.

= 20 × 100.

= 200.

Therefore there are 200 boys in the school.