Question
A man invests a total of Rs 40,000 in two schemes for 2
years: I) Scheme A: Simple interest at 8% p.a. II) Scheme B: Compound interest at 10% p.a., compounded annually. The total interest earned from both schemes after 2 years is Rs 7,400. How much money (in rupees) did he invest in Scheme A (simple interest)?Solution
ATQ, Let amount invested in Scheme A (SI) = x Then amount in Scheme B (CI) = 40,000 − x Interest from Scheme A (8% SI, 2 years): I_A = x × 8 × 2 /100 = 0.16x Interest from Scheme B (10% CI, 2 years): Amount factor for 10% for 2 years = 1.1² = 1.21 So interest factor = 1.21 − 1 = 0.21 I_B = (40,000 − x) × 0.21 = 8,400 − 0.21x Total interest: I_A + I_B = 0.16x + (8,400 − 0.21x) = 8,400 − 0.05x Given total interest = 7,400: 8,400 − 0.05x = 7,400 0.05x = 1,000 x = 1,000 / 0.05 = 20,000 So, Rs 20,000 was invested in Scheme A.
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