The mean of the marks obtained by $100$ students is $60 .$ If the marks obtained by one of the students was incorrectly calculated as $75$ whereas the actual marks obtained by him were $65,$ what is the correct mean of the marks obtained by the students?

The average weight of $3$ men $A, B$ and $C$ is $84 \,k g .$ Another man, $D,$ joins the group, and the average weight becomes $80\, kg .$ If another man, $E$, whose weight is $3 \,kg$ more than that of $D ,$ replaces $A$, then average weight of $B , C , D$ and $E$ becomes $79 \,kg$. The weight of $A$ is (in $kg$)

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 of marks obtained by $150$ candidates in a certain examination is $50 .$ If the average marks of passed candidates is $55$ and that of the failed candidates is $25,$ what is the number of candidates who passed the examination?

The average age of $35$ students in a class is $16\, years.$ The average age of $21$ students is $14$ What is the average age of remaining $14$ students ?(in $years$)