$A$ and $B$ started a business with initial investments in the ratio of $5:7$. If,after one year,their profits were in the ratio of $1:2$ and the period for $A$'s investment was $7$ months,for how many months did $B$ invest the money?

Two businessmen $A$ and $B$ invest in a business in the ratio $5:8$. They decided to reinvest $30\%$ of the profit they earned back into the business. The remaining profit they distributed amongst themselves. If $A$'s share of the profit was ₹ $87,500$,then how much total profit (in ₹) did the business make (in $,000$)?

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?

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

$A$ 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.

$A, B, C$ 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 $₹$):