$A$ 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)?

Aditya and Sanjay started a business investing $45000$ and $30000$ respectively. What will be the ratio between their profit?

$A$ 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?

Satheesh started a business investing ₹ $60000$. After $3$ months,Sunil joined him with a capital of ₹ $75000$. After another $6$ months,Subhash joined them with a capital of ₹ $105000$. At the end of the year,they made a profit of ₹ $19000$. Find the share of each.

Aditya and Manish continued in a joint business for $36$ months. Aditya contributed $Rs. 300$ for a certain time and Manish invested $Rs. 500$ for the remaining time. If out of a total profit of $Rs. 1020$,Aditya gets $Rs. 495$,then for how long (in months) did Aditya keep his money?

$A, B, C$ and $D$ enter into a partnership. $A$ contributes $\frac{1}{3}$ of the capital,$B$ contributes $\frac{1}{4}$,$C$ contributes $\frac{1}{5}$,and $D$ contributes the rest. What is the share (in ₹) of $D$ when the total profit is ₹ $6000$?