The ratio of boys to girls in a school is 7:5. If 20 more girls join the school, the new ratio of boys to girls becomes 7:6. What…

Question

The ratio of boys to girls in a school is 7:5. If 20 more girls join the school, the new ratio of boys to girls becomes 7:6. What is the total number of students in the school initially?

1. A. 200
2. B. 240 (Correct answer)
3. C. 300
4. D. 360

Correct Answer

Option B — 240

Detailed Solution & Explanation

The correct answer is 240.

Key Points

• Let boys and girls be 7x and 5x.
• After 20 girls join: $\dfrac{7x}{5x + 20} = \dfrac{7}{6}$.
• Cross-multiplying: $42x = 35x + 140$, so $7x = 140$ and x = 20.
• Boys $= 140$, girls $= 100$, so the initial total is 240.

Additional Information

• The number of boys is unchanged, which is why the boys' part of the ratio stays 7 — spotting that fixes the multiplier immediately.
• Verify: after the change there are 140 boys and 120 girls, and $140 : 120 = 7 : 6$ ✓
• The question asks for the initial total, not the final one — 260 would be the trap for anyone who adds the 20.

प्रश्न (हिन्दी में)

एक स्कूल में लड़कों और लड़कियों का अनुपात 7:5 है। यदि 20 और लड़कियाँ स्कूल में शामिल हो जाती हैं, तो लड़कों और लड़कियों का नया अनुपात 7:6 हो जाता है। शुरू में स्कूल में छात्रों की कुल संख्या कितनी थी?

1. A. 200
2. B. 240
3. C. 300
4. D. 360