$A$ man invested $Rs. 260000$ in $5\%$ stock at $104$. He sold the stock when the price rose to $Rs. 125$ and invested the sale proceeds in $6\%$ stock. By doing this,his income increased by $Rs. 2500$. At what price did he purchase the second stock? (in $Rs.$)

$A$ person invests $Rs.\, 28500$ in $5\%$ stock at $95$. He sold $Rs.\, 15000$ stock when the price rose to $Rs.\, 98$ and sold the remaining stock when the market value of the stock fell to $Rs.\, 90$. How much does he gain or lose in the transaction?

Find the income obtained by investing $Rs. 90000$ in $7 \frac{1}{2} \%$ stock at $112 \frac{1}{2}$ (in $Rs.$).

Find out the investment required to get an income of $Rs. 1938$ from $9 \frac{1}{2} \%$ stock at $90$ (Brokerage $1 \%$). (in $Rs.$)

In a business partnership among $A, B, C$ and $D,$ the profit is shared as follows: $\frac{A's \text{ share}}{B's \text{ share}} = \frac{B's \text{ share}}{C's \text{ share}} = \frac{C's \text{ share}}{D's \text{ share}} = \frac{1}{3}.$ If the total profit is $Rs. 4,00,000,$ the share of $C$ is (in $Rs.$):

Seema had $50$ preferred shares and $400$ common shares of par value $Rs. 100$ each. If the dividend declared on preferred shares is $10\%$ per annum and a semiannual dividend of $7.5\%$ is on common shares,find the annual dividend received by Seema (in $Rs.$).