The arithmetic mean of $100$ observations is $24$. If $6$ is added to each of the observations and then each of them is multiplied by $2.5$,find the new arithmetic mean.

In a class,there are $20$ boys whose average age is decreased by $2$ months,when one boy aged $18$ years is replaced by a new boy. The age of the new boy is:

The average age of a cricket team reduces by $2$ when two senior players aged $32$ and $30$ are replaced by $2$ youngsters of equal age. What is the age of these youngsters?

$A$ number,$x$,equals $80 \%$ of the average of $5, 7, 14$ and a number $y$. If the average of $x$ and $y$ is $26$,then the value of $y$ is:

The sum of five numbers is $260$. The average of the first two numbers is $30$ and the average of the last two numbers is $70$. What is the third number?

$A$ man spends $Rs. 1800$ monthly on an average for the first four months and $Rs. 2000$ monthly for the next eight months and saves $Rs. 5600$ a year. His average monthly income is (in $Rs.$)