$A$ 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?

$A$ batsman in his $17^{th}$ innings makes a score of $85$ runs,and thereby,increases his average by $3$ runs. What is his average after the $17^{th}$ innings? He had never been 'not out'.

It rained as much on Wednesday as on all the other days of the week combined. If the average rainfall for the whole week was $3 \, cm$,then how much did it rain on Wednesday? (in $cm$)

$10$ years ago,the average age of all $25$ teachers of a girls' college was $45$ years. $4$ years ago,the principal retired at the age of $60$ years. One year later,a new principal aged $54$ years was recruited. Considering the principal as a teacher,what is the present average age of all $25$ teachers?

The average of two numbers $A$ and $B$ is $20,$ that of $B$ and $C$ is $19,$ and that of $C$ and $A$ is $21.$ What is the value of $A?$

The average marks of $40$ students in an examination was $25$. It was later found that the marks of one student had been wrongly entered as $73$ instead of $37$. What is the value of the correct average?