The average age of a group of $9$ students is $20\, \text{years}$. When $6$ more students joined the group,the average age falls by $2\, \text{years}$. The average age of the new students is:

$A$ 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 salary of workers in $AMS$ careers is $Rs. 2,000$,the average salary of faculty is $Rs. 4,000$,and the average salary of management trainees is $Rs. 1,250$. The total number of workers could be:

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?

The average age of $5$ members is $21 \text{ years}$. If the age of the youngest member is $5 \text{ years}$,find out the average age of the family at the birth of the youngest member (in $\text{years}$).

The average of $8$ numbers is $20$. The average of the first two numbers is $15 \frac{1}{2}$ and that of the next three is $21 \frac{1}{3}$. If the sixth number is less than the seventh and eighth numbers by $4$ and $7$ respectively,then the eighth number is: