$30$ 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 two numbers $A$ and $B$ is $20,$ that of $B$ and $C$ is $19,$ and that of $C$ and $A$ is $21.$ What is the value of $A?$

$10$ years ago,the average age of a family of $4$ members was $24$ years. Two children have been born (with an age difference of $2$ years),and the present average age of the family remains the same. The present age of the youngest child is (in years):

$A$ group of boys has an average weight of $36 \,kg$. One boy weighing $42 \,kg$ leaves the group and another boy weighing $30 \,kg$ joins the group. If the average now becomes $35.7 \,kg$,then how many boys are there in the group?

If the difference between the average of $x, y$ and $y, z$ is $12,$ then the difference between $x$ and $z$ is

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