Discussion
Sakshi invests a part of Rs. 12,000 in 12% stock at Rs. 120 and the remainder in 15% stock at Rs. 125. If his total dividend per annum is Rs. 1360, how much does he invest in 12% stock at Rs. 120?
Answer: A
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 \( \tfrac{r}{m} \).
\[ \text{12\% at 120 yields } 10\%, \qquad \text{15\% at 125 yields } 12\% \]
\[ 0.10x + 0.12(12000 - x) = 1360 \]
\[ 0.10x + 1440 - 0.12x = 1360 \quad\Longrightarrow\quad -0.02x = -80 \]
\[ x = \text{Rs. } 4000 \]
Checking: Rs. 400 from the first stock and Rs. 960 from the Rs. 8000 in the second.
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