The sum of five numbers is $260$. The average of the first two numbers is $30$ and the average of the last two numbers is $70$. What is the third number?

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:

The average age of $8$ men is increased by $2$ years when $2$ of them,whose ages are $20$ years and $24$ years respectively,are replaced by $2$ women. What is the average age of these two women (in years)?

Out of three numbers,the first is twice the second and is half of the third. If the average of the three numbers is $56$,the three numbers in order are

The average of $50$ numbers is $38$. If two numbers,namely $45$ and $55$,are discarded,the average of the remaining numbers is

In a class,the average height of $35$ girls was measured as $160 \,cm$. Later,it was discovered that the height of one of the girls was misread as $144 \,cm$,while her actual height was $104 \,cm$. What was the actual average height of the girls in the class? (in $cm$) (rounded off to two digits after decimal)