$A$ man bought $20$ shares of $Rs. 100$ at $4$ discount,the rate of dividend being $12 \%$. The rate of interest obtained is (in $\%$):

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 $Rs.$)

$A$ company has issued $10000$ preferred shares and $50000$ common shares,both with a par value of $Rs. 100$ each. The dividend on a preferred share and a common share is $12 \%$ and $17.6 \%$,respectively. The company had a total profit of $Rs. 15$ Lakhs,out of which some amount was kept in a reserve fund and the remaining was distributed as a dividend. Find the amount (in Lakhs) kept in the reserve fund.

$A$ 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 $Rs.$)

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