The sum of the ages of father and son at present is $33 \, \text{years}$. Two years ago, the product of their ages was $28 \, \text{years}$. What is the age of the father and the son (in $\text{years}$)?

The average age of $8$ men is increased by $2\, \text{years}$ when two of them whose ages are $21\, \text{years}$ and $23\, \text{years}$ are replaced by two new men. The average age of the two new men is:

In a cricket team of $11$ boys,one player weighing $42 \,kg$ is injured and replaced by another player. If the average weight of the team is increased by $100 \,g$ as a result of this,then what is the weight of the new player (in $.1$)? (in $kg$)

The average of runs scored by a cricketer in his $99$ innings is $99$. How many runs will he have to score in his $100^{\text{th}}$ innings so that his average of runs in $100$ innings may be $100$?

The mean weight of $34$ students of a school is $42\, kg$. If the weight of the teacher is included, the mean weight increases by $400\, g$. Find the weight (in $kg$) of the teacher.

The average marks of students in an examination was $65$. It was later found that the marks of one student had been wrongly entered as $83$ instead of $38$. If there were $50$ students, what is the correct average?