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

The average age of $5$ members is $21 \text{ years}$. If the age of the youngest member is $5 \text{ years}$,find out the average age of the family at the birth of the youngest member (in $\text{years}$).

The average temperature from Monday to Wednesday is $37^{\circ}C$,while the average temperature from Tuesday to Thursday is $34^{\circ}C$. The temperature of Thursday is $\frac{4}{5}$ times that of Monday. Find the temperature of Thursday in $^{\circ}C$.

If the average of $6$ consecutive even numbers is $25,$ the difference between the largest and the smallest number is

There are three baskets of fruits. The $1^{st}$ basket has twice the number of fruits in the $2^{nd}$ basket. The $3^{rd}$ basket has three-fourths of the fruits in the first. The average of the fruits in all the baskets is $30$. What is the number of fruits in the first basket?

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.