Multiple choice

The compound interest and simple interest for two years on a certain sum of money at a certain rate of interest is 157.5. Find the principal if rate of interest is 15%. एक निश्चित धनराशि पर निश्चित ब्याज की दर से दो वर्षों के चक्रवृद्धि ब्याज और साधारण ब्याज में अंतर 157.5 है। मूलधन ज्ञात कीजिए यदि ब्याज की दर 15 प्रतिशत है।

  1. Rs. 6000

  2. Rs. 7000

  3. Rs. 8000

  4. Rs. 15750
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B Correct answer
Explanation

For 2 years, CI - SI = P × (r/100)^2. Given CI - SI = 157.5 and r = 15%. So 157.5 = P × (15/100)^2 = P × 0.0225. Therefore P = 157.5/0.0225 = 157.5 × 10000/225 = 1575000/225 = 7000. Verification: SI for 2 years = 7000 × 0.15 × 2 = 2100. CI for 2 years = 7000 × (1.15)^2 - 7000 = 9257.50 - 7000 = 2257.50. CI - SI = 2257.50 - 2100 = 157.50. ✓

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