$\mathrm{A}$ and $\mathrm{B}$ started a business by investing $\mathrm{Rs}.45000$ and $\mathrm{Rs}.60000$ respectively. By mistake, they divided the total profit in the ratio $1:3$. Then, $\mathrm{A}$ loses $\mathrm{Rs}.500.$ Find the total profit.

Three partners shared the profit in a business in the ratio $2:3:6$. They had partnered for $12$ months, $9$ months and $15$ months respectively. What was the ratio of their investments?

$\mathrm{A}$ and $\mathrm{B}$ started a business with initial investments in the ratio of $9:10$ and their annual profits were in the ratio $3:5$. If $\mathrm{A}$ invested the money for $8$ months, for how many months did $\mathrm{B}$ invest his money?

Prabha started a business investing $₹32000$. After $5$ months, Amit joined her with a capital $₹22000$. At the end of the year, the total profit was $₹16409$. What is Prabha's share of the profit?

$A, B$ and $C$ start a business each investing $Rs. 16000$. After $3$ months, $A$ withdrew $Rs. 2000$, $B$ withdrew $Rs. 4000$ and $C$ invests $Rs. 8000$ more. At the end of the year a total profit of $Rs. 41580$ was made. Find the share of $A$.