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

$A$ 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 invested $Rs. 14,400$ in $Rs. 100$ shares of a company at $20\%$ premium. If the company declares $5\%$ dividend at the end of the year,then how much does he get? (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 $110$?

Mrudul invested an amount of $Rs. 29500$ in order to start a business. Shalaka joined her $4$ months later by investing an amount of $Rs. 33500$. If the business earned a profit of $Rs. 120575$ at the end of two years,what was Mrudul's share of the profit? (in $Rs.$)