CAT 2025

Slot 1

QA

Question & SolutionQues & Sol

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

1. Concept Used

• Topic: Simple Interest / Weighted Returns on Investment (Arithmetic — Linear Equations)
• Formula: $$\text{Total Gain} = r_S \cdot S + r_B \cdot B + r_G \cdot G$$

where (S), (B), (G) are amounts invested in Stocks, Bonds, and Gold, and (r_S = 0.10), (r_B = 0.06), (r_G = 0.08) are their respective annual return rates.

2. Calculation

We are given three conditions:

$$S + B + G = 100000 \quad \text{...(i)}$$

$$B = 0.25G \quad \text{...(ii)}$$

$$0.10S + 0.06B + 0.08G = 8200 \quad \text{...(iii)}$$

From condition (ii), substitute (B = 0.25G) into condition (i):

$$S + 0.25G + G = 100000 \implies S = 100000 - 1.25G$$

Now substitute both (S = 100000 - 1.25G) and (B = 0.25G) into condition (iii):

$$0.10(100000 - 1.25G) + 0.06(0.25G) + 0.08G = 8200$$

$$10000 - 0.125G + 0.015G + 0.08G = 8200$$

$$10000 - 0.03G = 8200$$

$$0.03G = 1800 \implies G = 60000$$

Now find (B):

$$B = 0.25 \times 60000 = 15000$$

Gain from bonds:

$$\text{Gain}_{\text{bonds}} = 0.06 \times 15000 = 900$$

3. Solution

Answer = 900 ✅

The amount Kamala gained from her bond investment in one year is Rs 900.