Rohit started a business with $75000$ and after some months,Simran joined him with $60000$. If the profit at the end of the year is divided in the ratio $3:1$,then after how many months did Simran join Rohit?

$A$ and $B$ entered into a partnership with capitals in the ratio $4:5$. After $3$ months,$A$ withdrew $\frac{1}{4}$ of his capital and $B$ withdrew $\frac{1}{5}$ of his capital. The gain at the end of $10$ months was ₹ $760$. $A$'s share in the profit is (in ₹):

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?

Srikant and Vividh started a business investing amounts of $Rs. 185000$ and $Rs. 225000$,respectively. If Vividh's share in the profit earned by them is $Rs. 9000$,what is the total profit (in $Rs.$) earned by them together?

$A$ began a business with ₹ $3750$. $B$ joined later with ₹ $5000$. When did $B$ join if the profits at the end of the year were divided equally?

$A$, $B$ 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?