A batsman has a certain average of runs for $12$ innings. In the $13^{th}$ innings, he scores $96$ runs and thereby increasing his average by $5$ runs. What is his average after the $13^{th}$ innings ?

A professional institute's total expenditure on students for a particular course is partly fixed and partly varies linearly with the number of students. The average expense per student is $Rs.\,615$ when there are $24$ students and $Rs.\,465$ when there are $40$ students. What is the average expense when there are $60$ students ? (in $Rs.$)

The average of $50$ numbers is $38 .$ If two numbers, namely, $45$ and $55$ are discarded, what is the average of the remaining numbers ?

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 $Rs.$ )

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

What will be the average of even numbers between $11$ to $63 ?$