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 for a year. $A$ contributes $₹ 1500$ and $B$ $₹ 2000$. After $4$ months,they admit $C$,who contributes $₹ 2250$. If $B$ withdraws his contribution after $9$ months,how would they share a profit of $₹ 900$ at the end of the year?

$A, B, C$ enter into a partnership with shares in the ratio $\frac{7}{2}: \frac{4}{3}: \frac{6}{5}.$ After $4 \text{ months}$,$A$ increases his share by $50\%.$ If the total profit at the end of one year is $₹ 21600,$ then $B$'s share in the profit is (in $₹$):

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?

$A$ and $B$ started a partnership business by investing in the ratio of $3:8$. $C$ joined them after $4$ months with an amount equal to $\frac{3}{4}$ of $B$'s investment. What was the total profit (in ₹) at the end of the year if $C$ received ₹ $24000$ as his share?

Gupta and Bansal enter into a partnership with their capitals in the ratio $5:6$. At the end of $8$ months,Gupta withdraws his capital. If they receive their shares of profits in the ratio of $5:9$,find out how long (in months) Bansal's capital was invested in the business?