The arithmetic mean of $100$ observations is $24.6$ is added to each of the observations and, then each of them is multiplied by $2.5 .$ Find the new arithmetic mean.

$A , B , C$ and $D$ are four consecutive even numbers respectively and their average is $65 .$ What is the product of $A$ and $D ?$

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 ?

The average of marks of $28$ students in Mathematics was $50 .$ $8$ students left the school, then this average increased by $5 .$ What is the average of marks obtained by the students who left the school?

The average of $10$ mumbers is $7 .$ What will be the new average if each of the numbers is multiplied by $8 \,?$

The average age of four brothers is $12 \,year.$ If the age of their mother be also included, the average is increased by $5\, year.$ The age of the mother (in $years$) is