In a city, the current number of literate people is 25,000. If the number of literate males decreases by 5% and the number of lit…

Question

In a city, the current number of literate people is 25,000. If the number of literate males decreases by 5% and the number of literate females increases by 10%, the total literate population becomes 25,250. What is the present number of literate males in the city?

1. A. 12,500
2. B. 14,000
3. C. 15,000 (Correct answer)
4. D. 16,500

Correct Answer

Option C — 15,000

Detailed Solution & Explanation

The correct answer is 15,000.

Key Points

• Let literate males = m, so literate females = 25,000 − m.
• The net change is 25,250 − 25,000 = +250, so:
  • −0.05m + 0.10(25,000 − m) = 250
  • −0.05m + 2,500 − 0.10m = 250
  • −0.15m = −2,250 → m = 15,000
• So there are 15,000 literate males and 10,000 literate females.

Additional Information

• Check: males fall by 5% of 15,000 = 750; females rise by 10% of 10,000 = 1,000; net +250 ✓.
• Working with the net change rather than the new total keeps the numbers small and avoids carrying 25,250 through the algebra.
• The alligation method reaches the same answer: the overall change is +1% (250 on 25,000), sitting between −5% and +10%, so males : females = (10 − 1) : (1 − (−5)) = 9 : 6 = 3 : 2, giving 15,000 and 10,000.

प्रश्न (हिन्दी में)

एक शहर में वर्तमान में साक्षर लोगों की संख्या 25,000 है। यदि साक्षर पुरुषों की संख्या में 5% की कमी आती है और साक्षर महिलाओं की संख्या में 10% की वृद्धि होती है, तो कुल साक्षर जनसंख्या 25,250 हो जाती है। शहर में साक्षर पुरुषों की वर्तमान संख्या क्या है?

1. A. 12,500
2. B. 14,000
3. C. 15,000
4. D. 16,500