Question
A man invests ₹50,000 in two schemes A and B for 1
year. Scheme A offers 12% simple interest and Scheme B offers 10% compound interest, compounded annually. If the total interest earned from both schemes is ₹5,800, how much did he invest in scheme A?Solution
Let the amount invested in scheme A be ₹x. Then, the amount invested in scheme B is ₹50,000 - x. Interest from scheme A (simple interest) = P × R × T / 100 = x × 12 × 1 / 100 = 0.12x. Interest from scheme B (compound interest) = P(1 + R/100)^T - P = (50,000 - x)(1 + 10/100) – (50,000 - x) = (50,000 - x)(1.1) - (50,000 - x) = (50,000 - x) × 0.1. The total interest from both schemes is ₹5,800, so: 0.12x + (50,000 - x) × 0.1 = 5,800. 0.12x + 5,000 - 0.1x = 5,800, 0.02x = 800, x = 800 / 0.02 = ₹40,000. Thus, the amount invested in scheme A is ₹40,000. Correct option: d
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