The average age of a group of $15$ students is $10 \, \text{years}$. When $5$ more students joined the group,the average age increased by $1 \, \text{year}$. If the average age of the $5$ new students is $x$,find the value of $x$ (in $\text{years}$).

The sum of three consecutive odd numbers is $38$ more than the average of these numbers. What is the first of these numbers?

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?

The average contribution of $5$ men to a fund is $Rs.\,35.$ $A$ sixth man joins and pays $Rs.\,35$ more than the resultant average of $6$ men. The total contribution of all the six men is (in $Rs.$)

Of the three numbers,the first is twice the second and the second is thrice the third. If the average of the three numbers is $10$,the numbers are

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