Three partners shared the profit in a business in the ratio $5: 7: 8$. They had partnered for $14$ months,$8$ months,and $7$ months respectively. What was the ratio of their investments?

Arun,Kamal,and Vinay invested ₹ $8000$,₹ $4000$,and ₹ $8000$ respectively in a business. Arun left after six months. If after eight months,there was a gain of ₹ $4005$,then what will be the share of Kamal (in ₹)?

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?

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).

$P$ 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 $B$ enter into a partnership; $A$ invests ₹ $50$ and $B$ invests ₹ $45$. At the end of $4$ months,$A$ withdraws half his capital and at the end of $5$ months,$B$ withdraws $\frac{1}{2}$ of his capital. $C$ then enters with a capital of ₹ $70$. At the end of $12$ months,the total profit is ₹ $254$. How should the profit be divided among $A$,$B$,and $C$?