The frequency distribution data is given below. If the average age is $17 \text{ years}$,the value of $m$ is:

Age (in years)	$8, 20, 26, 29$
Number of People	$3, 2, m, 1$

$A$ batch of $60$ students made an average score of $50$ marks and another batch of $40$ students made an average score of $45$ marks. What is the overall average score?

The average weight of $3$ men $A, B$ and $C$ is $84 \, kg$. Another man $D$ joins the group and the average now becomes $80 \, kg$. If another man $E$,whose weight is $3 \, kg$ more than that of $D$,replaces $A$,then the average weight of $B, C, D$ and $E$ becomes $79 \, kg$. The weight of $A$ is (in $kg$)

The average age of $10$ men is increased by $2 \, \text{years}$ when one of them, aged $25 \, \text{years}$, is replaced by a new man. What is the age of the new man (in $\text{years}$)?

Visitors to a show were charged $Rs. 15.00$ each on the first day,$Rs. 7.50$ on the second,and $Rs. 2.50$ on the third day. The total attendance of visitors for the three days was in the ratio $2:5:13$. Find the average charge per visitor for the entire show (in $Rs.$).

There were $35$ students in a hostel. If the number of students increases by $7$,the expenses of the mess increase by $Rs. 42$ per day while the average expenditure per head decreases by $Rs. 1$. Find the original expenditure of the mess in $Rs$.