$A$ 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 ₹)?

$A$ 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)?

Sita and Gita enter into a partnership. Sita contributes ₹ $5,000$ while Gita contributes ₹ $4,000$. After $1$ month,Gita withdraws $\frac{1}{4}$ part of her contribution and after $3$ months,Sita invests ₹ $2,000$ more. When Gita withdraws her investment,at the same time,Rita joins them by investing ₹ $7,000$. If at the end of $1$ year there is a profit of ₹ $1,218$,what will be the share of Rita in the profit (in ₹)?

$A$,$B$,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 $A$?

$A, B, C$ 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 ₹ $6000$?

Aditya,Manish,and Gaurav enter into a partnership with shares in the ratio of $\frac{7}{2} : \frac{4}{3} : \frac{6}{5}$. After $4$ months,Aditya increases his share by $50\%$. If at the end of one year the total profit is $Rs. 43200$,then what will be Manish's share in the profit?