Kamala divided her investment of Rs 100000 between stocks, bonds, and gold. Her investment in bonds was 25% of her investment in gold. With annual returns of 10%, 6%, 8% on stocks, bonds, and gold, respectively, she gained a total amount of Rs 8200 in one year. The amount, in rupees, that she gained from the bonds, was:
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Correct Answer: 900
Solution and Explanation
Step 2: Substitute \(G = 4B\) into the investment equation. \[ S + B + 4B = 100000 \Rightarrow S + 5B = 100000 \Rightarrow S = 100000 - 5B. \]
Step 3: Substitute into the gain equation. \[ 0.10(100000 - 5B) + 0.06B + 0.08(4B) = 8200. \] Expand: \[ 10000 - 0.50B + 0.06B + 0.32B = 8200. \] Combine like terms: \[ 10000 - 0.12B = 8200. \]
Step 4: Solve for \(B\). \[ 10000 - 8200 = 0.12B \Rightarrow 1800 = 0.12B \Rightarrow B = \frac{1800}{0.12} = 15000. \] Thus, investment in bonds is \(15000\) rupees.
Step 5: Compute gain from bonds. \[ \text{Gain} = 0.06 \times 15000 = 900. \] Therefore, the amount Kamala gained from bonds is: \[ \boxed{900}. \]
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