Simple Interest and Compound Interest Question 3 - CAT 2025
Kamala divided her investment of Rs. 100,000 between stocks, bonds, and gold. Her investment in bonds was 25% of her investment in gold. With annual returns of 10%, 6%, and 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:
Step-by-Step Explanation
Let the allocations for Stocks, Bonds, and Gold be S, B, and G, respectively.
Investment Relations:
S + B + G = 100,000
We are told that investment in bonds is 25% of gold:
B = 0.25G → G = 4B
Expressing Variables in Terms of B:
Substitute G = 4B into the total sum:
S + B + 4B = 100,000
S + 5B = 100,000
S = 100,000 − 5B
Set up the Return Equation:
The total return from all three assets is Rs. 8200:
0.10S + 0.06B + 0.08G = 8200
Substitute the expressions for S and G:
0.10(100,000 − 5B) + 0.06B + 0.08(4B) = 8200
10,000 − 0.50B + 0.06B + 0.32B = 8200
10,000 − 0.12B = 8200
0.12B = 1800
B = 1800 / 0.12 = 15,000
Find the Interest Earned from Bonds:
Bond Earnings = 6% of 15,000
= 0.06 × 15,000
= Rs. 900
Correct Answer: 900
💡 FundaMakers Tip: When a linear system contains multiple variables bound together by percentages, choose the variable with the most connections as your single anchor. Here, relating both Stocks and Gold directly back to Bonds () reduces a three-variable system down to a simple single-variable linear equation, making the algebra fast and error-free.
Simple Interest and Compound Interest Shortcuts & Tricks
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