Discussion
Rs. 9800 are invested partly in 9% stock at 75 and 10% stock at 80 to have equal amount of incomes. The investment in 9% stock is:
Answer: B
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 \( \tfrac{r}{m} \).
\[ \text{9\% at 75 yields } \frac{9}{75} = 12\%, \qquad \text{10\% at 80 yields } \frac{10}{80} = 12.5\% \]
Equal incomes from the two parts:
\[ 0.12x = 0.125(9800 - x) \]
\[ 0.12x = 1225 - 0.125x \quad\Longrightarrow\quad 0.245x = 1225 \]
\[ x = \text{Rs. } 5000 \]
Each part then yields Rs. 600.
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