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 $,000$)?

Two partners invested ₹ $12500$ and ₹ $8500$ in a business. They decided that $60 \%$ of the profit incurred from the business will be equally divided between them,while the remaining profit will be distributed as interest on their capitals. If one of the partners receives ₹ $300$ more profit than the other,what is the total profit (in ₹) in the business?

$A$ starts a business with $Rs. 4000$ and $B$ joins him after $3$ months with $Rs. 16000$. Find the ratio of their profits at the end of the year.

$P$ and $Q$ enter into a partnership. $P$ invests $Rs. 50$ and $Q$ invests $Rs. 45$. At the end of $4$ months,$P$ withdraws half of his capital,and at the end of the $5^{\text{th}}$ month,$Q$ withdraws half of his capital. $S$ then enters the partnership with a capital of $Rs. 70$. At the end of $12$ months,they earn a total profit of $Rs. 1272.5$. What was $S$'s share in the profit?

$A$ 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 $C$?

Anju and Brijesh enter into a partnership with their capitals in the ratio of $5:9$. At the end of $8$ months,Anju withdraws her capital. If they receive their share of profit in the ratio of $4:9$,find out how long Brijesh's capital was invested in the business (in months).