Question

The ratio of the number of boys and girls in a class is 13 ∶ 8. If 50 boys leave the class and 50 girls enter the class, then their ratio will be 4 ∶ 3. Find the final number of girls.
1. 400
2. 500
3. 450
4. 350

Answer 1

Correct Answer - Option 3 : 450

Given:

Initial ratio of boys and girls = 13 : 8

50 boys leave the class and 50 girls enter the class

The final ratio of boys and girls = 4 : 3

Calculation:

Let initial number of boys and girls be 13x and 8x respectively.

50 boys leave the class and 50 girls enter the class,

So 13x - 50 and 8x + 50

As per question,

⇒ (13x - 50)/(8x + 50) = 4/3

⇒ 39x - 32x = 200 + 150 

⇒ 7x = 350

⇒ x = 50

Final number of girls is 8x + 50

⇒ 8 × 50 + 50

⇒ 450

∴ Final number of girls is 450.