Discussion
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:
Answer: D
In stock problems, a "\( r\% \) stock at \( m \)" means Rs. 100 of face value costs Rs. \( m \) and pays Rs. \( r \) a year, so the yield on money invested is \( \tfrac{r}{m} \).
\[ \text{9\% at 96 yields } \frac{9}{96} = \frac{3}{32}, \qquad \text{12\% at 120 yields } \frac{12}{120} = \frac{1}{10} \]
Equal dividends:
\[ x \times \frac{3}{32} = y \times \frac{1}{10} \quad\Longrightarrow\quad \frac{x}{y} = \frac{32}{30} = \frac{16}{15} \]
The investments are in the inverse ratio of the yields, so the lower-yielding stock takes the larger sum.
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