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?

There are $35$ students in a hostel. If the number of students increased by $7$,the expenses of the mess were increased by $Rs. 42$ per day while the average expenditure per head decreased by $Rs. 1$. Find out the actual expenditure of the mess (in $Rs.$).

$A$ student bought $4$ books for $Rs. 120$ from one book shop and $6$ books for $Rs. 150$ from another. The average price (in rupees),he paid per book was

The mean daily profit made by a shopkeeper,in a month of $30$ days,was $Rs. 350$. If the mean profit for the first $15$ days was $Rs. 275$,then the mean profit for the last $15$ days would be (in $Rs.$)

Average age of $15$ students of a class is $15 \text{ years}$. Out of these,the average age of $5$ students is $14 \text{ years}$ and that of the other $9$ students is $16 \text{ years}$. The age of the $15^{th}$ student is (in $\text{years}$):

The average age of a group of $9$ students is $20\, \text{years}$. When $6$ more students joined the group,the average age falls by $2\, \text{years}$. The average age of the new students is: