$A$, $B$ 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?

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 $B$ invest in a business in the ratio of $3:2$. If $5\%$ of the total profit goes to charity and $A$'s share is $₹ 855$,then the total profit is (in $₹$):

Anil and Nikhil started a business by investing $Rs. 3300$ and $Rs. 5000$ respectively. If they earned a profit of $Rs. 1660$,what will be Anil's share?

How many statements are required to find: What is the amount invested in Scheme $B$?
$I$. The amounts invested in Schemes $A$ and $B$ are in the ratio of $2:3$.
$II$. The amount invested in Scheme $A$ is $40\%$ of the total amount invested.
$III$. The amount invested in Scheme $A$ is ₹ $45,000$.