Gupta and Bansal enter into a partnership with their capitals in the ratio $5:6$. At the end of $8$ months,Gupta withdraws his capital. If they receive their shares of profits in the ratio of $5:9$,find out how long (in months) Bansal's capital was invested in the business?

Shekhar started a business investing ₹ $25000$ in $1999$. In $2000$,he invested an additional amount of ₹ $10000$ and Rajeev joined him with an amount of ₹ $35000$. In $2001$,Shekhar invested another additional amount of ₹ $10000$ and Jatin joined them with an amount of ₹ $35000$. What will be Rajeev's share in the profit (in ₹) of ₹ $150000$ earned at the end of $3$ years from the start of the business in $1999$?

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 $Rs$)?

$A$ starts a business with a capital of ₹ $1200$. $B$ and $C$ join with some investments after $3$ and $6$ months,respectively. If,at the end of a year,the profit is divided in the ratio of $2:3:5$,what is $B$'s investment (in ₹) in the business?

$A$ and $B$ start a business with investments of ₹ $5000$ and ₹ $4500$ respectively. After $4$ months,$A$ takes out half of his capital. After two more months,$B$ takes out one-third of his capital while $C$ joins them with a capital of ₹ $7000$. At the end of a year,they earn a profit of ₹ $5080$. Find the share of each member in the profit.

$P$ 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?