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?

$A, B$ and $C$ entered into a partnership in the ratio $\frac{1}{2}: \frac{1}{3}: \frac{1}{4}$. After $2$ months,$A$ withdraws half of his capital and after $10$ months,a profit of ₹ $378$ is divided among them. What is $B$'s share (in ₹)?

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 ₹)?

$A$ and $B$ entered into a partnership investing ₹ $16000$ and ₹ $12000$ respectively. After $3$ months,$A$ withdrew ₹ $5000$ while $B$ invested ₹ $5000$ more. After another $3$ months,$C$ joined the business with a capital of ₹ $21000$. If the total profit after $1$ year is ₹ $26400$,by how much does the share of $B$ exceed that of $C$?

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?

$A$ 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.