A sum of money is equally divided among a number of children. Had there been 10 children less, each would have received ₹ 5 more, and had there been 10 children more, each would have received ₹ 3 less. What is the sum of money that is distributed?एक धनराशि कुछ बच्चों में बराबर बाँटी जाती है। यदि 10 बच्चे कम होते, तो प्रत्येक को ₹ 5 अधिक मिलते, और यदि 10 बच्चे अधिक होते, तो प्रत्येक को ₹ 3 कम मिलते। वितरित की गई धनराशि कितनी है?

1. A₹ 300
2. B₹ 600
3. C₹ 750
4. D₹ 900

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Correct answer: B. ₹ 600

Explanation

Let n children share ₹ S. S/(n−10) − S/n = 5 gives 10S = 5n(n−10); S/n − S/(n+10) = 3 gives 10S = 3n(n+10). So 5(n−10) = 3(n+10) → n = 40, and S = 5 × 40 × 30 / 10 = ₹ 600. Check: 600/40 = 15, 600/30 = 20 (+5), 600/50 = 12 (−3).मान लीजिए n बच्चे ₹ S बाँटते हैं। S/(n−10) − S/n = 5 से 10S = 5n(n−10); S/n − S/(n+10) = 3 से 10S = 3n(n+10)। अतः 5(n−10) = 3(n+10) → n = 40, और S = 5 × 40 × 30 / 10 = ₹ 600। जाँच: 600/40 = 15, 600/30 = 20 (+5), 600/50 = 12 (−3)।