Three years ago,the average age of a family of $5$ members was $27 \text{ years}$. After the addition of a child to the family,the present average age of the family is still $27 \text{ years}$. Find the present age of the child (in years).

$A$ student finds the average of ten $2$-digit numbers. While copying the numbers,by mistake,he writes one number with its digits interchanged. As a result,his answer is $1.8$ less than the correct answer. The difference between the digits of the number in which he made the mistake is:

In a school with $600$ students,the average age of the boys is $12$ $years$ and that of the girls is $11$ $years$. If the average age of the school is $11$ $years$ and $9$ $months$,then the number of girls in the school is:

The average of runs of a cricket player in $10$ innings was $32$. How many runs must he make in his next innings so as to increase his average of runs by $4$?

The average weight of $8$ persons increases by $2.5\, kg$ when a new person comes in place of one of them weighing $65\, kg$. What is the weight of the new person? (in $kg$)

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