The average age of $10$ men is increased by $2 \, \text{years}$ when one of them, aged $25 \, \text{years}$, is replaced by a new man. What is the age of the new man (in $\text{years}$)?

The average age of a group of $15$ students is $10 \, \text{years}$. When $5$ more students joined the group,the average age increased by $1 \, \text{year}$. If the average age of the $5$ new students is $x$,find the value of $x$ (in $\text{years}$).

The average marks obtained by a class of $60$ students is $65$. The average marks of half of the students is found to be $85$. The average marks of the remaining students is:

$10 \, kg$ of rice priced at $Rs. \, 12$ per $kg$ is mixed with $6 \, kg$ of rice priced at $Rs. \, 16$ per $kg$. Find the average price in $Rs.$ per $kg$ of the whole mixture?

The average weight of $10$ students is increased by $0.5 \, kg$ when one of the students weighing $50 \, kg$ is replaced by a new student. Find the weight of the new student (in $kg$).

$A$ person travels $\frac{1}{3}$ of his journey by bus at $60\, km/h$,$\frac{1}{3}$ by scooter at $30\, km/h$,and the rest by walking at $10\, km/h$. Find his average speed for the whole journey (in $km/h$).