Question

The ratio of boys and girls in a school is 7 : 9. If 40 boys join the school and 40 girls leave the school, the ratio becomes 9 : 7. The number of boys initially in the school is?    
1. 180
2. 140
3. 220
4. 160

Answer 1

Correct Answer - Option 2 : 140

Given:

The original ratio = 7 : 9

Number of boys joined = 40

Number of girls left = 40

The changed ratio = 9 : 7

Calculation:

Let the no. of boys be 7x

So, the no. of girls = 9x

According to the question,

(7x + 40)/(9x - 40) = 9/7

⇒ 49x + 280 = 81x - 360

⇒ 32x = 640 

⇒ x = 20

So, the no. of boys = 7 × 20 = 140

∴ The number of boys in the school is 140