The average of three consecutive odd numbers is $12$ more than one-third of the first of these numbers. What is the last of the three numbers?

The average weight of $100$ students is $32\, kg$. The average weight of the first $49$ students is $30\, kg$ and that of the last $50$ students is $34\, kg$. What is the weight (in $kg$) of the $50^{th}$ student?

The mean of $100$ items was $46$. Later on,it was discovered that an item $16$ was misread as $61$ and another item $43$ was misread as $34$. It was also found that the number of items was $90$ and not $100$. Then,what is the correct mean?

In an examination,the average marks were found to be $60$. The marks of $80$ candidates had to be changed from $95$ to $70$ each,and the average came down to $55$ marks. The total number of candidates who attended the examination was:

$A$ librarian purchased $50$ storybooks for his library. He realized that he could get $14$ more books by spending $Rs. 76$ more,and the average price per book would be reduced by $Rs. 1$. What was the average price (in $Rs.$) of each book he initially bought?

$A$ cricketer has a certain average for $10$ innings. In the eleventh inning,he scored $108$ runs,thereby increasing his average by $6$ runs. His new average is