The average weight of $15$ oarsmen in a boat is increased by $1.6\, kg$ when one of the crew,who weighs $42\, kg$,is replaced by a new man. Find the weight of the new man (in $kg$).

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?

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 average pocket money of $3$ friends $A, B,$ and $C$ is $Rs. 80$ per month. If $B$ spends double and $C$ spends triple of what $A$ spends during that month,and if the average of their unspent pocket money is $Rs. 60,$ then how much does $A$ spend (in $Rs.$)?

The average marks of Sameer decreased by $1,$ when he replaced the subject in which he scored $40$ marks with two other subjects in which he scored $23$ and $25$ marks respectively. Later,he also included $57$ marks of Computer Science,and the average marks increased by $2.$ How many subjects were there initially?

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