The average weight of five persons sitting in a boat is $38\, kg$. The average weight of the boat and the persons sitting in the boat is $52\, kg$. What is the weight of the boat (in $kg$)?

The average age of a group of persons going for a picnic is $16.75 \text{ years}$. $20$ new persons with an average age of $13.25 \text{ years}$ join the group on the spot,due to which the average age of the group becomes $15 \text{ years}$. Find the number of persons initially going for the picnic.

The mean of the marks obtained by $100$ students is $60$. If the marks obtained by one of the students was incorrectly calculated as $75$ whereas the actual marks obtained by him were $65$,what is the correct mean of the marks obtained by the students?

The average weight of $24$ students in section $A$ of a class is $58 \,kg,$ whereas the average weight of $26$ students in section $B$ of the same class is $60.5 \,kg$. Find out the average weight of all the $50$ students of the class. (in $kg$)

The average score of Rahul,Manish,and Suresh is $63$. Rahul's score is $15$ less than Ajay and $10$ more than Manish. 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?

In a set of prime and composite numbers,the number of composite numbers is twice the number of prime numbers,and the average of all the numbers in the set is $9$. If the number of prime numbers and composite numbers are exchanged,then the average of the set of numbers increases by $2$. If,during the exchange of the numbers,the average of the prime numbers and composite numbers individually remained constant,then what was the ratio of the average of composite numbers to the average of prime numbers (initially)?