Ram started a business by investing $Rs. 45000$. After $3$ months,Sanjay joined him with a capital of $Rs. 60000$. After $6$ months,Aditya joined them with a capital of $Rs. 90000$. At the end of the year,they earned a profit of $Rs. 16500$. What is Ram's share in the business (in $Rs.$)?

Anil and Nikhil started a business by investing $Rs. 3300$ and $Rs. 5000$ respectively. If they earned a profit of $Rs. 1660$,what will be Anil's share?

$A, B$ and $C$ entered into a partnership by investing ₹ $12000$, ₹ $15000$ and ₹ $18000$ respectively. $A$ is also a working partner and receives $15 \%$ of the annual profit for his work. If $B$ and $C$ received ₹ $8500$ and ₹ $10200$ from the annual profit as their shares, what amount did $A$ receive from the annual profit?

Aditya,Manish,and Gaurav enter into a partnership with shares in the ratio of $\frac{7}{2} : \frac{4}{3} : \frac{6}{5}$. After $4$ months,Aditya increases his share by $50\%$. If at the end of one year the total profit is $Rs. 43200$,then what will be Manish's share in the profit?

Rohit started a business with $75000$ and after some months,Simran joined him with $60000$. If the profit at the end of the year is divided in the ratio $3:1$,then after how many months did Simran join Rohit?

$P, Q$ and $R$ invested their capital in the ratio of $8:6:5$. At the end of the business,they received the profit in the ratio of $1:3:5$. Find the ratio of time for which they contributed their capital.