Multiple choice

The difference between the simple and the compound interest on a certain sum of money at 4% per annum in 3 years is Rs. 30.4. What is the sum? एक धनराशि पर 4% प्रति वर्ष की दर से 3 वर्ष में साधारण व चक्रवृद्धि ब्याज का अन्तर 30.4 रू. है। धनराशि क्या है?

  1. Rs. 5000

  2. Rs. 6000

  3. Rs. 7500

  4. Rs. 6250
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D Correct answer
Explanation

For 3 years at r%: CI - SI = P[(1 + r)³ - 1 - 3r] = P[(1.04)³ - 1 - 0.12] = P[1.124864 - 1.12] = P(0.004864) = 30.4. Therefore P = 30.4/0.004864 = 6250. Verification: CI = 6250(1.04)³ - 6250 = 780.4; SI = 6250 × 0.04 × 3 = 750; difference = 30.4 ✓. Key distractor: 6000 (uses simple approximation).

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