$A$ 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 $\%$):

Find out the income percent on $10 \%$ debentures of par value $Rs.\, 120$ available in the market for $Rs.\, 150$. (in $\%$)

Find the annual dividend received by Nishita from $1200$ preferred shares and $3000$ common shares,both of par value $Rs. 50$ each,if the dividend paid on preferred shares is $10 \%$ and a semi-annual dividend of $3 \frac{1}{2} \%$ is declared on common shares. (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?

$A$ man invested $Rs. 50490$ in $5\%$ stock at $99$ and sold it when the price rose to $Rs. 102$. He invested the sale proceeds in $8\%$ stock at $96$. Find out the change in the man's income (Brokerage: $Rs. 3$).

$A$ 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 $\%$).