How should a profit of ₹ $450$ be divided between two partners,one of whom has contributed ₹ $1200$ for $5$ months and the other ₹ $750$ for $4$ months?

$A$ 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)?

$A$ began a business with ₹ $85000$. He was joined afterwards by $B$ with ₹ $42500$. For how much period (in months) does $B$ join,if the profits at the end of the year are divided in the ratio of $3:1$?

$A$ and $B$ started a partnership business investing some amount in the ratio of $3: 5$. $C$ joined them after six months with an amount equal to that of $B$. In what proportion should the profit at the end of one year be distributed among $A, B$ and $C$?

$A$ and $B$ start a business with investments of ₹ $5000$ and ₹ $4500$ respectively. After $4$ months,$A$ takes out half of his capital. After two more months,$B$ takes out one-third of his capital while $C$ joins them with a capital of ₹ $7000$. At the end of a year,they earn a profit of ₹ $5080$. Find the share of each member in the profit.

Rahul started a business by investing $Rs. 45,000$. $6$ months later,Sanjay joined him with $Rs. 30,000$. In what ratio should the earned profit be distributed at the end of the year?