$A$,$B$ and $C$ start a business. If the ratio of their periods of investments is $2: 3: 6$ and their profits are in the ratio of $4: 5: 6$, then the ratio of capitals of $A$,$B$ and $C$ is

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

$P, Q$ and $R$ invested their capital in the ratio of $8:6:5$. At the end of the business,they received the profit in the ratio of $1:3:5$. Find the ratio of time for which they contributed their capital.

$A$ 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)?

$A$ 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 ₹)?

$A, B, C$ enter into a partnership with shares in the ratio $\frac{7}{2}: \frac{4}{3}: \frac{6}{5}.$ After $4 \text{ months}$,$A$ increases his share by $50\%.$ If the total profit at the end of one year is $₹ 21600,$ then $B$'s share in the profit is (in $₹$):