The average of $11$ numbers is $10.9$. If the average of the first six is $10.5$ and the average of the last six is $11.4$, find the middle (sixth) number.

If the mean of $a, b, c$ is $M$ and $ab + bc + ca = 0$,then the mean of $a^2, b^2, c^2$ is

Five years ago,the average age of a husband and wife was $23 \text{ years}$. Today,the average age of the husband,wife,and child is $20 \text{ years}$. How old is the child in years?

If the average of $m$ numbers is $n^{2}$ and that of $n$ numbers is $m^{2}$,then the average of $(m + n)$ numbers is

Of the three numbers, the second is twice the first and thrice the third. If the average of the three numbers is $44$, then the largest number is

The average marks obtained by $150$ students in an examination is $40$. If the average marks of passed students is $60$ and that of the failed students is $20$,what is the number of students who passed the examination?