$A, B$ and $C$ enter into a partnership by investing ₹ $35000$,₹ $45000$ and ₹ $55000$ respectively. What are the respective shares of $A, B$ and $C$ in an annual profit of ₹ $40500$?

Sita and Gita invested the same capital in a business. At the year-end,they shared the profit in the ratio of $3:2$. If Sita invested her capital for the whole year,for how many months did Gita invest her capital?

Ram,Karan,and Rohan invested capital in the ratio of $2:3:4$ for time periods of $6:4:3$. Find the ratio of profit distributed.

$A$ 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.

$P$ 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 $B$ enter into a partnership. $A$ supplies the whole capital of ₹ $45000$ with the condition that the profits are to be equally distributed,$B$ pays $A$ interest on half of the capital at $10 \%$ per annum,and $B$ receives ₹ $120$ per month for managing the business. If $B$'s total income is $\frac{1}{2}$ of $A$'s total income,what is their total yearly profit (in ₹)?