# The ratio of boys and girls in a school is 5 ∶ 7. If, in the next session, 250 boys and 450 girls join the school, the ratio of boys and girls becomes

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The ratio of boys and girls in a school is 5 ∶ 7. If, in the next session, 250 boys and 450 girls join the school, the ratio of boys and girls becomes 2 ∶ 3. How many girls are in the school now?
1. 1200
2. 1500
3. 1000
4. 1600

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Correct Answer - Option 2 : 1500

Given:

The ratio of number of boys and girls = 5 : 7

In the next session, 250 boys and 450 girls joined

Calculation:

Let the ratio of boys and girls be 5x : 7x

According to the question

$\dfrac{5x \ + \ 250}{7x \ + \ 450} = \dfrac{2}{3}$

⇒ 15x + 750 = 14x + 900

⇒ x = 150

The number of girls now

7 × 150 + 450 = 1500

∴ The number of girls now is 1500.