$A$ batsman has a certain average in $11$ innings. In the $12^{\text{th}}$ innings,he scores $90$ runs and his average decreases by $5$. After the $12^{\text{th}}$ innings,what is his average?

The average contribution of $5$ men to a fund is $Rs.\,35.$ $A$ sixth man joins and pays $Rs.\,35$ more than the resultant average of $6$ men. The total contribution of all the six men is (in $Rs.$)

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 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?

$A$ team of $8$ persons participates in a shooting competition. If the best marksman had scored $92$ points instead of $85$ points, the average score for the team would have been $84$. What was the total number of points the team actually scored?

The average of two numbers is $62$. If $2$ is added to the smaller number,the ratio between the numbers becomes $1:2$. The smaller number is