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

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 $\text{years}$)?

The arithmetic mean of the scores of a group of students in a test was $52$. The brightest $20\%$ of them secured a mean score of $80$ and the dullest $25\%$ a mean score of $31$. The mean score of the remaining $55\%$ is

Find the average of the following set of scores: $253, 124, 255, 534, 836, 375, 101, 443, 760$.

The average age of a committee of $8$ members is $40 \text{ years}$. $A$ member,aged $55 \text{ years}$,retired and was replaced by a member aged $39 \text{ years}$. The average age of the present committee is (in $\text{years}$):

The average of $3$ numbers is $22$. If the first number is $\frac{3}{8}$ of the sum of the other two numbers,what is the first number?