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.
$30$
$75$
$35$
$60$
The average of $13$ results is $60 .$ If the average of first $7$ results is $59$ and that of last $7$ results is $61,$ what will be the seventh result $?$
The average of first three numbers is double of the fourth number. If the average of all the four numbers is $12,$ find the $4^{th}$ number.
The average of two numbers is $62 .$ If $2$ is added to the smaller number, the ratio between the numbers becomes $1: 2 .$ The smaller number is
It rained as much on Wednesday as on all the others days of the week combined. If the average rainfall for the whole week was $3 \,cm $ then how much did it rain on Wednesday? (in $cm$)
In a school, the average age of students is $6 \,years$ , and the average age of $12$ teachers is $40\, years.$ If the average age of the combined group of all the teachers and students is $7 \,years$ , then the number of students is?