A man invests some money partly in 9% stock at 96 and partly in 12% stock at 120. To obtain equal dividends from both, he must invest the money in the ratio

### Concept & Logic When the income (dividend) from two different investments is equal, their investment amounts are inversely proportional to their respective yields. $$ \text{Yield} = \frac{\text{Dividend \%}}{\text{Market Value}} $$ ### Step-by-Step Solution 1. **Given:** - Stock 1: 9% at 96 - Stock 2: 12% at 120 - Income 1 = Income 2 2. **Calculate Income in terms of Investments:** - Let the investment in Stock 1 be $x$ and in Stock 2 be $y$. - Income from Stock 1 = $\frac{9}{96} \times x = \frac{3}{32}x$ - Income from Stock 2 = $\frac{12}{120} \times y = \frac{1}{10}y$ 3. **Equate the Incomes:** - $\frac{3}{32}x = \frac{1}{10}y$ 4. **Find the Ratio $x : y$:** - $\frac{x}{y} = \frac{32}{3 \times 10} = \frac{32}{30}$ - Simplify the fraction by dividing by 2: - $\frac{x}{y} = \frac{16}{15}$ ### Exam Strategy & Shortcut Equate the fractions directly and flip: Investment Ratio = $\text{Yield}_2 : \text{Yield}_1 = \left( \frac{12}{120} \right) : \left( \frac{9}{96} \right) = \frac{1}{10} : \frac{3}{32} = 32 : 30 = 16 : 15$. ### Common Pitfall Forgetting to simplify the fractions before determining the ratio, which can lead to calculation errors or unlisted options. ### Final Answer Therefore, the correct answer is **16 : 15**.