$A$ certain sum is divided among $A, B$ and $C$ in such a way that $A$ gets $Rs. 40$ more than $\frac{1}{2}$ of the sum. $B$ gets $Rs. 120$ less than $\frac{3}{8}$ of the sum,and $C$ gets $Rs. 200$. What is the total sum in $Rs.$?

Brij has $800$ shares of par value $Rs. 50$ each and $600$ debentures of par value $Rs. 100$ each of the company. The company pays an annual dividend of $6 \%$ on the shares and interest of $12 \%$ on the debentures. Find out the total annual income of Brij (in $Rs.$) and the rate of return on his investment (in $\%$).

$A$ medicine company issued $125000$ shares of par value $Rs. 20$ each. If the total dividend declared by the company is $Rs. 375000$,find out the rate of dividend paid by the company (in $\%$).

$A$ 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 $Rs.$)

$A$ man invests $Rs. 27600$ in $4 \%$ stock at $92$. He sold $Rs. 20000$ stock when the price rose to $Rs. 96$,and sold the remaining stock when the market value fell to $Rs. 90$. How much does he gain or loss in the transaction?

What investment will be required to purchase $Rs.\, 90000$ of $8 \%$ stock at $110$?