CAT 2025 Slot 1 QA Question & Solution

ArithmeticHard

Question

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

Solution

Let the amounts invested in Stocks be S, Bonds B, and, Gold be G

Given that $$S + B + G = 100000, B = 0.25G$$

$$0.10S + 0.06B + 0.08G = 8200$$

Substitute S = 100000 - B - G = 100000 - 1.25G

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

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

$$10000 - 0.03G = 8200$$

$$ 0.03G = 1800 \Rightarrow G = 60000$$

$$B = 0.25G = 15000$$

Gain from bonds = $$0.06 \times 15000 = 900$$