Vijay invested certain amounts of money in two schemes $A$ and $B$, which offer interest at the rate of 8% per annum and 9% per annum, respectively. He received ₹1,860 as the total annual interest. However, had he interchanged the amounts of investments in the two schemes, he would have received ₹20 more as annual interest. How much money did he invest in each scheme?
Generated by claude-sonnet-4-6 · 2026-06-15 10:32 · grounding rag
Model Answer
Let amount invested in Scheme A = ₹x and in Scheme B = ₹y.
Equation 1 (original investment):
$$\frac{8x}{100} + \frac{9y}{100} = 1860$$
$$\Rightarrow 8x + 9y = 186000 \tag{1}$$
Equation 2 (interchanged investment gives ₹20 more):
$$\frac{9x}{100} + \frac{8y}{100} = 1880$$
$$\Rightarrow 9x + 8y = 188000 \tag{2}$$
Elimination Method:
Multiply (1) by 9 and (2) by 8:
$$72x + 81y = 1674000 \tag{3}$$
$$72x + 64y = 1504000 \tag{4}$$
Subtract (4) from (3):
$$17y = 170000 \Rightarrow y = 10000$$
Substitute y = 10000 in (1):
$$8x + 90000 = 186000 \Rightarrow 8x = 96000 \Rightarrow x = 12000$$
∴ Vijay invested ₹12,000 in Scheme A and ₹10,000 in Scheme B.
Verification: 8% of 12000 + 9% of 10000 = 960 + 900 = ₹1860 ✓
Source: Pair of Linear Equations in Two Variables, Section 3.3.2 (Elimination Method)
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Explanation
- Form both equations carefully from the given conditions — this earns the first 2 marks.
- Use the elimination method (as taught in §3.3.2): multiply to equalise coefficients, then subtract.
- Always verify your answer — CBSE awards 1 mark for correct verification in 5-mark word problems.
- The key insight: interchanging amounts increases interest by ₹20, so the second equation uses 1860 + 20 = 1880.