In a school, the average age of students is $6 \, \text{years}$, and the average age of $12$ teachers is $40 \, \text{years}$. If the average age of the combined group of all the teachers and students is $7 \, \text{years}$, then the number of students is?

The average of $5$ quantities is $6$. The average of three of them is $8$. What is the average of the remaining two quantities?

The average weight of a group of $20$ boys was calculated to be $89.4 \, kg$ and it was later discovered that one weight was misread as $78 \, kg$ instead of $87 \, kg$. The correct average weight is (in $kg$).

$A$ professional institute's total expenditure on students for a particular course is partly fixed and partly varies linearly with the number of students. The average expense per student is $Rs.\,615$ when there are $24$ students and $Rs.\,465$ when there are $40$ students. What is the average expense when there are $60$ students? (in $Rs.$)

Eleven years earlier,the average age of a family of $4$ members was $28 \, \text{years}$. Now,the average age of the same family with $6$ members is still the same,even though $2$ children were born in this period. If they belong to the same parents and the age of the first child at the time of the birth of the younger child was the same as the total number of family members just after the birth of the youngest member,then what is the present age of the youngest member of the family in years?

$A$ batsman has an average of $30$ runs in his $42$ innings. The difference between his maximum and minimum score is $100$. If these two innings are removed,his average for $40$ innings comes down to $28$. What is his minimum score?