$A$ and $B$ enter into a partnership with capitals in the ratio $5: 6$. At the end of $8$ months,$A$ withdraws. If they receive profits in the ratio $5: 9$,find how long $B$'s capital was used (in months)?

Arvind began a business with ₹ $550$. Later,Brij joined with ₹ $330$. When did Brij join if the profit at the end of the year was divided in the ratio $10:3$?

$A$ and $B$ invest in a business in the ratio $4:5$. After $10$ months,$B$ leaves the business after withdrawing his investment. In the first year,the business made a profit of ₹ $49,000$. What is $A$'s share (in ₹) of this profit?

In a business,$A$ and $C$ invested amounts in the ratio $2:1,$ whereas the ratio between amounts invested by $A$ and $B$ was $3:2$. If ₹ $1,57,300$ was their total profit,how much amount (in ₹) did $B$ receive?

Nikita and Nishita enter into a partnership by investing ₹ $50,000$ and ₹ $40,000$ respectively. They agreed to share profits in the ratio of their capitals. Find out the share of Nikita when the total profit of the business is ₹ $22,500$ after a year.

Simran started a software business by investing ₹ $50000$. After six months,Nanda joined her with a capital of ₹ $80000$. After $3$ years,they earned a profit of ₹ $24500$. What was Simran's share in the profit? (In ₹)