After replacing an old member with a new member,it was found that the average age of five members of a club is the same as it was $3 \, \text{years}$ ago. What is the difference between the ages of the replaced member and the new member (in $\text{years}$)?

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?

Refer to the line graph and answer the given question.
Number of candidates who qualified in a given competitive examination from $6$ states during two given years.
What is the average number of candidates who qualified in the given competitive exam from states $Q, S, T$ and $U$ in $2004$?

The average of $6$ numbers is $20$. If one number is removed, the average becomes $15$. What is the number removed?

The average price per $kg$ of rice at $10$ different places was $Rs. 4.85$. After a week,the price per $kg$ was increased by $20$ paise at $3$ places and decreased by $10$ paise at $1$ place. What is the new average price per $kg$ in $Rs.$?

$16$ children are to be divided into two groups $A$ and $B$ of $10$ and $6$ children. The average percent marks obtained by the children of group $A$ is $75$ and the average percent marks of all the $16$ children is $76$. What is the average percent marks of children of group $B$?