The average of a non-zero number and its square is $5$ times the number. The number is

There are $6$ consecutive odd numbers in increasing order. The difference between the average of the squares of the first $4$ numbers and the last $4$ numbers is $64$. If the sum of the squares of the first and the last element is $178$,then the average of all the $6$ numbers is:

The average of a collection of $20$ measurements was calculated to be $56 \, cm$. But later,it was found that a mistake had occurred in one of the measurements which was recorded as $64 \, cm$,but should have been $61 \, cm$. The correct average must be? (in $cm$)

The average age of a group of $9$ students is $20\, \text{years}$. When $6$ more students joined the group,the average age falls by $2\, \text{years}$. The average age of the new students is:

$12 \%$ of Kaushal's monthly salary is equal to $16 \%$ of Nandini's monthly salary. Suresh's monthly salary is half that of Nandini's monthly salary. If Suresh's annual salary is $Rs.\, 1.08$ lakhs,what is Kaushal's monthly salary in $Rs.$?

Nine friends have a dinner in a hotel. Eight of them spent $Rs. 12$ each on their meals and the ninth spent $Rs. 16$ more than the average expenditure of all the nine. Find out the total money in $Rs.$ spent by them?