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

$A$ 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 $Rs.$)

Mac buys $200$ shares of par value $Rs. 10$ each,of a company,which pays an annual dividend of $8 \%$ at such a price that he gets $10 \%$ on his investment. Find the market value of one share (in $Rs.$).

$A$ man sells $5000$ common shares of Company $X$ (each of par value $Rs. 10$), which pays a dividend of $20\%$, at $Rs. 30$ per share. He invests the sale proceeds in ordinary shares of Company $Y$ (each of par value $Rs. 25$) that pays a dividend of $15\%$. If the market value of a share of Company $Y$ is $Rs. 40$, find out the number of shares of Company $Y$ purchased by the man.

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

The cost price of a $Rs. 100$ stock at $4$ discount,when brokerage is $\frac{1}{4}\%$ is (in $Rs.$)