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 $Rs.$).

Find the income on $7 \frac{1}{2} \%$ stock of $Rs.\, 20000$ purchased at $Rs.\, 120$. (in $Rs.$)

$A$ 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 $\%$):

$A$ and $B$ started a business by investing $Rs. 18,000$ and $Rs. 24,000$ respectively. At the end of the $4^{\text{th}}$ month from the start of the business,$C$ joins with $Rs. 15,000$. At the end of the $8^{\text{th}}$ month,$B$ quits,at which time $C$ invests $Rs. 3,000$ more. At the end of the $10^{\text{th}}$ month,$B$ rejoins with the same investment. If the profit at the end of the year is $Rs. 12,005$,what is $B$'s share of profit? (in $Rs.$)

The capital of a company is made up of $50000$ preferred shares with a dividend of $20 \%$ and $20000$ common shares,the par value of each type of share being $Rs. 10$. The company had a total profit of $Rs. 180000$,out of which $Rs. 30000$ were kept in a reserve fund and the remaining was distributed to shareholders. Find the dividend percentage for the common shareholders (in $\%$).

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