$A$,$B$,and $C$ rented a pasture. $A$ puts in $12$ oxen for $6 \text{ months}$,$B$ puts in $8$ oxen for $7 \text{ months}$,and $C$ puts in $6$ oxen for $8 \text{ months}$. If the total rent of the field is ₹ $396$,what amount (in ₹) of rent was paid by $A$?

$A$ 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 ₹)?

$A$ 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?

$A$ and $B$ invest in a business in the ratio $4:5$. After $10$ months,$B$ leaves the business after withdrawing his investment. In the first year,the business made a profit of ₹ $49,000$. What is $A$'s share (in ₹) of this profit?

Two friends $P$ and $Q$ started a business investing in the ratio of $5:6$. $R$ joined them after six months investing an amount equal to that of $Q$. At the end of the year,$20\%$ profit was earned which was equal to $₹ 98000$. What was the amount invested by $R$?

$A, B$ 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 ₹ $40500$?