The average age of $35$ students in a class is $16$ years. The average age of $21$ students is $14$ years. What is the average age of the remaining $14$ students (in years)?

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

The average marks in English of a class of $24$ students is $56$. If the marks of three students were misread as $44, 45,$ and $61$ in lieu of the actual marks $48, 59,$ and $67$ respectively,then what would be the correct average?

$A$ batsman has an average of $30$ runs in his $42$ innings. The difference between his maximum and minimum score is $100$. If these two innings are removed,his average for $40$ innings comes down to $28$. What is his minimum score?

The average age of a group of $18$ persons is $32$ $years$ and $6$ $months$. If two persons of age $65$ $years$ each and one person of age $50$ $years$ leave the group,the average age of the remaining persons in the group will be (in $years$)

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 $100$. What is the correct mean?