The sum of five numbers is $260$. The average of the first two numbers is $30$ and the average of the last two numbers is $70$. What is the third number?

Of three numbers,the second is thrice the first and the third number is three-fourths of the first. If the average of the three numbers is $114$,the largest number is

The average of three consecutive odd numbers is $52$ more than $\frac{1}{3}$ of the largest of these numbers. What is the smallest of these numbers?

The average of $10$ numbers is $7$. What will be the new average if each of the numbers is multiplied by $8$?

The average weight of $25$ persons is increased by $1 \, kg$ when one man weighing $60 \, kg$ is replaced by a new person. What is the weight of the new person (in $kg$)?

In a school, the average age of students is $6 \, \text{years}$, and the average age of $12$ teachers is $40 \, \text{years}$. If the average age of the combined group of all the teachers and students is $7 \, \text{years}$, then the number of students is?