Of the three numbers whose average is $60$,the first is one-fourth of the sum of the others. The first number is

The average weight of $3$ persons is $65 \, kg$. If a fourth person having a weight of $45 \, kg$ joins the group,what is the average weight of the group? (in $kg$)

The sum of three numbers is $98$. If the ratio between the first and second is $2:3$ and that between the second and the third is $5:8$,then the second number is

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

The average age of a class of $30$ students and a teacher reduces by $0.5 \, \text{years}$ if we exclude the teacher. If the initial average is $14 \, \text{years}$,find the age of the class teacher in $\text{years}$.

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.