The average weight of $25$ persons is increased by $1 \, kg$ when one man weighing $60 \, kg$ is replaced by a new person. What is the weight of the new person (in $kg$)?

The average weight of $36$ students is $50 \,kg$. It was found later that the weight of one of the students was misread as $73 \,kg$,whereas his actual weight was $37 \,kg$. Find the correct average (in $kg$).

In a class of $100$ students,the mean marks obtained in a subject is $30$ and in another class of $50$ students the mean marks obtained in the same subject is $60$. The mean marks obtained by the students of two classes taken together is

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 average of $25$ consecutive odd integers is $55$. The highest of these integers is

In a competitive examination,the average marks obtained was $45$. It was later discovered that there was some error in computerization and the marks of $90$ candidates had to be changed from $80$ to $50$,and the average came down to $40$ marks. The total number of candidates appeared in the examination is