Find the investment required to purchase $Rs.\, 125000$ of $8 \%$ stock at $92$. (in $Rs.$)

$A$ 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 obtained by investing $Rs. 90000$ in $7 \frac{1}{2} \%$ stock at $112 \frac{1}{2}$ (in $Rs.$).

$A$ man sells $5000$ common shares of Company $X$ (each of par value $Rs. 10$), which pays a dividend of $20\%$, at $Rs. 30$ per share. He invests the sale proceeds in ordinary shares of Company $Y$ (each of par value $Rs. 25$) that pays a dividend of $15\%$. If the market value of a share of Company $Y$ is $Rs. 40$, find out the number of shares of Company $Y$ purchased by the man.

$A$ person buys $9 \frac{1}{2} \%$ stock of $Rs.\, 72000$ at $144$. Find his annual income (in $Rs.$).

What is a better investment,$4 \%$ stock at $Rs. 120$ or $3 \%$ stock at $Rs. 80$?