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

The average weight of all the $11$ players of the Indian cricket team is $50 \, kg$. If the average weight of the first six lightest players is $49 \, kg$ and that of the six heaviest players is $52 \, kg$,find the weight of the player who is in the sixth position when all $11$ players are arranged in order of increasing weights (in $kg$).

The average earning of a mechanic for the first four days of a week is $Rs. 18$ and for the last four days is $Rs. 22$. If he earns $Rs. 20$ on the fourth day,his average earning for the whole week is (in $Rs.$)

The average of $6$ numbers is $8$. What is the $7^{th}$ number so that the average becomes $10$?

The average age of a class of $30$ students and a teacher reduces by $0.5 \, \text{years}$ if we exclude the teacher. If the initial average is $14 \, \text{years}$,find the age of the class teacher in $\text{years}$.

The average age of three boys is $15$ years. If the ratio of their ages is $3:5:7$,what is the age of the oldest boy in years?