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    Question

    A certain sum of money is invested in two schemes:

    • Scheme A: Compound interest at 10% per annum, compounded annually, for 3 years. • Scheme B: Simple interest at 12% per annum for 4 years, on the same principal. The interest earned from Scheme B exceeds the interest earned from Scheme A by Rs. 1,490. Find the principal and also the total interest earned from both schemes together.
    A Principal = Rs. 15,000; total interest = Rs. 4,110 Correct Answer Incorrect Answer
    B Principal = Rs. 10,000; total interest = Rs. 8,110 Correct Answer Incorrect Answer
    C Principal = Rs. 20,000; total interest = Rs. 18,100 Correct Answer Incorrect Answer
    D Principal = Rs. 11,000; total interest = Rs. 8,010 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let principal = P. Interest from Scheme A (CI @ 10% for 3 years): CI = P[(1.10)^3 − 1] = P(1.331 − 1) = 0.331P. Interest from Scheme B (SI @ 12% for 4 years): SI = P × (12 × 4)/100 = 0.48P. Given: 0.48P − 0.331P = 1,490 0.149P = 1,490 P = 1,490 / 0.149 = 10,000. Now: Interest from Scheme A = 0.331 × 10,000 = Rs. 3,310. Interest from Scheme B = 0.48 × 10,000 = Rs. 4,800. Total interest from both schemes = 3,310 + 4,800 = Rs. 8,110. Answer: Principal = Rs. 10,000; total interest = Rs. 8,110.

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