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 $Rs.$).

How many shares of market value $Rs. 25$ each can be purchased for $Rs. 12750$,given that the brokerage is $2\%$?

$A$ started a business. After $4$ months from the start of the business,$B$ and $C$ joined. The respective ratio between the investments of $A, B$,and $C$ was $4: 6: 5$. If $A$'s share in the annual profit was $Rs. 250$ more than $C$'s share,what was the total annual profit earned? (in $Rs.$)

Find the income on $7 \frac{1}{2} \%$ stock of $Rs.\, 20000$ purchased at $Rs.\, 120$. (in $Rs.$)

Find the income on $12\%$ stock of $Rs.\, 60000$ purchased at $Rs.\, 110$. (in $Rs.$)

$A$ man bought $20$ shares of $Rs. 50$ at $5$ discount,the rate of discount being $4 \frac{3}{4} \%$. The rate of interest obtained is (in $\%$):