Question : A man invests half his capital at the rate of 10% per annum, one-third at 9% and the rest at 12% per annum. The average rate of interest per annum, which he gets, is:
Option 1: 9%
Option 2: 10%
Option 3: 10.5%
Option 4: 12%
Correct Answer: 10%
Solution : Use: Simple Interest = $\frac{\text{Principle × Rate × Time}}{100}$ and Average rate of interest = $\frac{\text{Total Interest}}{100×\text{Principal}}$ Let the total amount = Rs. $x$ Given: A man invests half his capital at the rate of 10% per annum, one-third at 9%. Remaining amount = $x-(\frac{x}{2}+\frac{x}{3})$ = $\frac{x}{6}$ Average rate of interest = $\frac{\frac{x}{2}×10+\frac{x}{3}×9+\frac{x}{6}×12}{x\times 100}$ = $\frac{5x+3x+2x}{x} \times 100$ = $\frac{10x}{x\times 100}\times 100$ = 10% Hence, the correct answer is 10%.
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