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.

The average salary per head of all the workers in a workshop is $Rs. 850$. If the average salary per head of $7$ technicians is $Rs. 1000$ and the average salary per head of the rest is $Rs. 780$,find out the total number of workers in the workshop.

In the first $10$ overs of a cricket game,the run rate was only $3.2$. What should be the run rate in the remaining $40$ overs to reach the target of $282$ runs?

$A$ cricketer had a certain average of runs for his $64$ innings. In his $65^{th}$ innings,he is bowled out for no score on his part. This brings down his average by $2$ runs. What is his new average of runs?

The average monthly salary of all the employees in an industry is $Rs. 12,000$. The average salary of male employees is $Rs. 15,000$ and that of female employees is $Rs. 8,000$. What is the ratio of male employees to female employees?

The average age of a group of $15$ students is $10 \, \text{years}$. When $5$ more students joined the group,the average age increased by $1 \, \text{year}$. If the average age of the $5$ new students is $x$,find the value of $x$ (in $\text{years}$).