$A$ and $B$ are partners in a business. $A$ contributes $\frac{1}{4}$ of the capital for $15$ months and $B$ received $\frac{2}{3}$ of the profit. For how long was $B$'s money used (in months)?

$A, B$ and $C$ together start a business. Three times the investment of $A$ equals four times the investment of $B$ and the capital of $B$ is twice that of $C$. The ratio of the share of each in the profit is

$A$ 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)?

$A$ 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.

$A$, $B$ 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 $B$ jointly invest ₹ $2100$ and ₹ $3100$ in a firm. $A$ is an active partner,hence he receives $25 \%$ of the profit separately. If their business yields ₹ $1040$ as profit,what will be the profit share for each of them?