The average score of Rahul,Manish,and Suresh is $63$. Rahul's score is $15$ less than Ajay's and $10$ more than Manish's. If Ajay scored $30$ marks more than the average score of Rahul,Manish,and Suresh,what is the sum of Manish's and Suresh's scores?

$A$ 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 ₹)?

Anil,Nikhil,and Saurabh started a business in partnership by investing in the ratio of $6:5:8$ respectively. At the end of the year,they earned a profit of $Rs. 83,600$. What will be Saurabh's share (in $Rs.$)?

$A$ and $B$ enter into a partnership for a year. $A$ contributes $₹ 1500$ and $B$ $₹ 2000$. After $4$ months,they admit $C$,who contributes $₹ 2250$. If $B$ withdraws his contribution after $9$ months,how would they share a profit of $₹ 900$ at the end of the year?

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?

Ravi and Kavi start a business by investing $Rs. 8000$ and $Rs. 72000$,respectively. Find the ratio of their profits at the end of the year. (in $:9$)