$A$, $B$ and $C$ invested capitals in the ratio $3: 5: 9$; the timing of their investments being in the ratio $2: 3: 1$. In what ratio would their profits be distributed?

$A$ 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)?

$P$ 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?

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 ₹)?

Rajan and Sajan started a business initially with $Rs. 14200$ and $Rs. 15600$ respectively. If the total profit at the end of the year is $Rs. 74500$,what is Rajan's share in the profit (in $Rs$)?