The average of the test scores of a class of $m$ students is $70$ and that of $n$ students is $91$. When the scores of both the classes are combined,the average is $80$. What is $n / m$?

The average weight of three boys $A, B$ and $C$ is $54 \frac{1}{3} \, kg,$ while the average weight of three boys $B, D$ and $E$ is $53 \, kg.$ What is the average weight of $A, B, C, D$ and $E$ (in $kg$)?

$A$ student was asked to find the arithmetic mean of the numbers $3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14$ and $x$. He found the mean to be $12$. What should be the number in place of $x$?

The average of marks obtained by $120$ candidates was $35.$ If the average of marks of passed candidates was $39$ and that of failed candidates was $15,$ the number of candidates who passed the examination is

$A$ group of boys has an average weight of $36 \,kg$. One boy weighing $42 \,kg$ leaves the group and another boy weighing $30 \,kg$ joins the group. If the average now becomes $35.7 \,kg$,then how many boys are there in the group?

Out of $30$ teachers of a school,a teacher of age $60$ $years$ retired. In his place another teacher of age $30$ $years$ was appointed. As a result,the mean age of the teachers will