The average weight of $6$ persons is increased by $5 \, kg$ when one of them who weighs $40 \, kg$ is replaced by a new man. The weight of the new man is (in $kg$):

Three years ago,the average age of a family of $5$ members was $17$ years. $A$ baby having been born,the average age of the family is the same today. The present age of the baby is (in years):

Find the average of all prime numbers between $60$ and $90$.

The average age of $A, B, C, D$ five years ago was $45$ years. By including $x$,the present average age of all the five is $49$ years. The present age of $x$ is (in years):

$30$ pens and $75$ pencils altogether were purchased for $Rs. \, 510$. If the average price of $75$ pencils was $Rs. \, 2$,then what was the average price of a pen? (in $Rs.$)

The average of $50$ numbers is $38$. If two numbers $45$ and $55$ are discarded,the average of the remaining set of numbers is: