The average weight of a class of $24$ students is $35 \, kg$. If the weight of the teacher is included, the average weight increases by $400 \, g$. The weight of the teacher is (in $kg$):

In a family,the average age of father and mother is $38 \text{ years}$,whereas the average age of father,mother,and their only daughter is $28 \text{ years}$. Then,the age of the daughter is? (in $\text{years}$)

The average weight of $45$ students in a class is $52 \, kg.$ Five of them whose average weight is $48 \, kg$ leave the class and other $5$ students whose average weight is $54 \, kg$ join the class. What is the new average weight (in $kg$) of the class?

The average age of Donald,his wife,and their two children is $23 \text{ years}$. His wife is $4 \text{ years}$ younger than Donald,and his wife was $24 \text{ years}$ old when his daughter was born. He was $32 \text{ years}$ old when his son was born. What is the average age of Donald and his daughter? (in $\text{years}$)

Average age of $15$ students of a class is $15 \text{ years}$. Out of these,the average age of $5$ students is $14 \text{ years}$ and that of the other $9$ students is $16 \text{ years}$. The age of the $15^{th}$ student is (in $\text{years}$):

The arithmetic mean of the scores of a group of students in a test was $52$. The brightest $20\%$ of them secured a mean score of $80$ and the dullest $25\%$ a mean score of $31$. The mean score of the remaining $55\%$ is