The average weight of $100$ students is $32\, kg$. The average weight of first $49$ students is $30\, kg$ and that of last $50$ students is $34\, kg$. What is the weight (in $kg$ ) of the $50^{ th }$ student ?

A person travelled from one place to another at an average speed of $40 \,km / h$ and back to the original place at an average speed of $50\, km / h$. What is his average speed in $km / h$ during the entire trip?

The average age of $5$ members is $21 \,years.$ If the age of the youngest member be $5 \,years,$ find out the average age of the family at the birth of the youngest member.(in $years$)

In the first $30$ overs of a cricket match, the run rate was $5.2 \,runs/over.$ What is the required run rate in the remaining $20$ overs to reach the target of $280$ runs?

The average of $100$ observations was calculated as $35.$ It was found later, that one of the observations was misread as $83$ instead of $53 .$ The correct average is