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:

$A$ batsman makes a score of $270$ runs in the $87^{th}$ inning and thus increases his average by a certain number of runs that is a whole number. Find the possible values of the new average.

$30$ pens and $75$ pencils altogether were purchased for $Rs. \, 510$. If the average price of $75$ pencils was $Rs. \, 2$,then what was the average price of a pen? (in $Rs.$)

The average marks of Sameer decreased by $1,$ when he replaced the subject in which he scored $40$ marks with two other subjects in which he scored $23$ and $25$ marks respectively. Later,he also included $57$ marks of Computer Science,and the average marks increased by $2.$ How many subjects were there initially?

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 of the teacher (in $kg$).

Three years ago,the average age of a family of $5$ members was $17$ years. $A$ baby having been born,the average age of the family is the same today. The present age of the baby is (in years):