The average of $50$ numbers is $30.$ If two numbers,$35$ and $40$ are discarded,then the average of the remaining numbers is nearly.

The average age of $24$ boys and their teacher is $15 \text{ years}$. When the teacher's age is excluded,the average age decreases by $1 \text{ year}$. What is the age of the teacher in years?

The average weight of $8$ sailors in a boat is increased by $1 \, kg$ if one of them weighing $56 \, kg$ is replaced by a new sailor. The weight of the new sailor is (in $kg$):

The average of marks obtained by $100$ candidates in a certain examination is $30$. If the average marks of passed candidates is $35$ and that of the failed candidates is $10$,what is the number of candidates who passed the examination?

The mean weight of $34$ students of a school is $42\, kg$. If the weight of the teacher is included, the mean weight increases by $400\, g$. Find the weight (in $kg$) of the teacher.

The average of two numbers $A$ and $B$ is $20,$ that of $B$ and $C$ is $19,$ and that of $C$ and $A$ is $21.$ What is the value of $A?$