$A$ 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 of a collection of $20$ measurements was calculated to be $56 \, cm$. But later,it was found that a mistake had occurred in one of the measurements which was recorded as $64 \, cm$,but should have been $61 \, cm$. The correct average must be? (in $cm$)

The average weight of $3$ persons is $65 \, kg$. If a fourth person having a weight of $45 \, kg$ joins the group,what is the average weight of the group? (in $kg$)

The average of four consecutive odd numbers is $40$. What is the largest number?

The average of five consecutive odd integers is $27$. What is the product of the first and the last number?

The average of marks obtained by $120$ candidates was $35.$ If the average of marks of passed candidates was $39$ and that of failed candidates was $15,$ the number of candidates who passed the examination is