An amount of Rs. 12200 is partly invested in scheme A at 10% p.a. on compound…
2024
An amount of Rs. 12200 is partly invested in scheme A at 10% p.a. on compound interest for two years and in scheme B at the same rate on simple interest for four years. If the interest received from both the schemes is equal, then find the amount invested in scheme A?
- A.
Rs.4350
- B.
Rs.4340
- C.
Rs.4200
- D.
Rs.8000
- E.
Rs.8500
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Correct answer: D
Concept: For a principal P at rate r% for time t, the Compound Interest over 2 years = P[(1 + r/100)2 − 1], and the Simple Interest = P × r × t / 100. When a total sum is split into two parts whose interests must be equal, equate the two interest expressions and solve the resulting linear equation for the unknown part.
Let the amount invested in scheme A be Rs. x; then scheme B receives Rs. (12200 − x).
Interest from A (compound, 10% p.a., 2 years) = x[(1 + 10/100)2 − 1] = x(1.21 − 1) = 0.21x.
Interest from B (simple, 10% p.a., 4 years) = (12200 − x) × 10 × 4 / 100 = 0.40 × (12200 − x).
Equate the interests: 0.21x = 0.40 × (12200 − x) → 0.21x = 4880 − 0.40x → 0.61x = 4880 → x = 4880 / 0.61 = 8000.
Cross-check: Interest from A = 0.21 × 8000 = Rs. 1680; Interest from B = 0.40 × (12200 − 8000) = 0.40 × 4200 = Rs. 1680. Both interests are equal, so the amount invested in scheme A is Rs. 8000.