$A$ 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?

The average weight of $4$ men $A, B, C,$ and $D$ is $67 \, kg.$ When a $5^{th}$ man $E$ is included,the average weight decreases by $2 \, kg.$ $A$ is replaced by $F.$ The weight of $F$ is $4 \, kg$ more than $E.$ The average weight decreases because of the replacement of $A,$ and now the average weight is $64 \, kg.$ Find the weight of $A.$

What is the age of a class teacher?
$I.$ There are $11$ students in the class.
$II.$ The average age of the students and the teacher is $14$ years.
$III.$ The average age of the teacher and the students is $3$ years more than that of the students.

The average of six numbers is $32$. If each of the first three numbers is increased by $2$ and each of the remaining three numbers is decreased by $4$,then the new average is?

Visitors to a show were charged $Rs. 15$ each on the first day,$Rs. 7.50$ on the second day,$Rs. 2.50$ on the third day,and the total attendance on the three days was in the ratio $2:5:13$ respectively. The average charge per person for the entire three days is (in $Rs.$):

$A$ cricketer whose bowling average is $12.4$ runs per wicket takes $5$ wickets for $26$ runs and thereby decreases his average by $0.4$. The number of wickets taken by him till the last match was: