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 nine numbers is $50$. The average of the first five numbers is $54$ and that of the last three numbers is $52$. Then the sixth 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 average of $6$ numbers is $20$. If one number is removed, the average becomes $15$. What is the number removed?

The average of $3$ numbers is $22$. If the first number is $\frac{3}{8}$ of the sum of the other two numbers,what is the first number?

There are three baskets of fruits. The $1^{st}$ basket has twice the number of fruits in the $2^{nd}$ basket. The $3^{rd}$ basket has three-fourths of the fruits in the first. The average of the fruits in all the baskets is $30$. What is the number of fruits in the first basket?