The average of the first $n$ consecutive even numbers is $101$. Find their sum.

The average of $13$ results is $60$. If the average of the first $7$ results is $59$ and that of the last $7$ results is $61$,what will be the seventh result?

The average weight of $36$ students is $50 \,kg$. It was found later that the weight of one of the students was misread as $73 \,kg$,whereas his actual weight was $37 \,kg$. Find the correct average (in $kg$).

In a coconut grove,$(x+2)$ trees yield $60$ nuts per year,$x$ trees yield $120$ nuts per year,and $(x-2)$ trees yield $180$ nuts per year. If the average yield per year per tree is $100$,find the value of $x$.

The average of a non-zero number and its square is $5$ times the number. The number is

The average age of a family of $6$ members $4$ years ago was $25$ years. Meanwhile,a child was born in this family,and the average age of the whole family is still the same today. The present age of the child in years is?