$A$ 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 $Rs.$?

$A$ company issued $50000$ shares of par value $Rs. 100$ each. If the total dividend declared by the company is $Rs. 125000$,out of which $Rs. 50000$ have been kept in reserve fund and the remaining is distributed as dividend,find out the rate of dividend paid by the company (in $\%$).

$A$ man bought $Rs. 20000$ of $5\%$ stock at $90$ and sold it when its price rose to $Rs. 93 \frac{3}{4}$. Find out his gain percent.

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

Anu invested $Rs.\, 32400$ in $8 \%$ stock at $90$. She sold $Rs.\, 18000$ stock when the price rose to $Rs.\, 95$ and the remaining stock at $Rs.\, 98$. She invested the total sale proceeds in $10 \%$ stock at $96 \frac{1}{2}$. Find the change in income of Anu (in $Rs.$).

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