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).

The average of runs scored by a cricketer in his $99$ innings is $99$. How many runs will he have to score in his $100^{\text{th}}$ innings so that his average of runs in $100$ innings may be $100$?

The average age of $8$ members of a group is $40 \text{ years}$. The age of $1$ member is $55 \text{ years}$. After his retirement,a new member of age $39 \text{ years}$ joins the group. What is the effect of this replacement on the average age of the group?

The average marks of students in an examination was $65$. It was later found that the marks of one student had been wrongly entered as $83$ instead of $38$. If there were $50$ students, what is the correct average?

Visitors to a show were charged $Rs. 15$ each on the first day,$Rs. 7.50$ on the second day,$Rs. 2.50$ on the third day,and the total attendance on the three days was in the ratio $2:5:13$ respectively. The average charge per person for the entire three days is (in $Rs.$):

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 $kg$)