The average of $11$ results is $50$. If the average of the first six results is $49$ and that of the last six is $52$,the sixth result is:

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

In a coconut grove,$(x+2)$ trees yield $60$ nuts per year,$x$ trees yield $120$ nuts per year,and $(x-2)$ trees yield $180$ nuts per year. If the average yield per year per tree is $100$,find the value of $x$.

$A$ person travelled from one place to another at an average speed of $40 \, km/h$ and back to the original place at an average speed of $50 \, km/h$. What is his average speed in $km/h$ during the entire trip?

The mean of $50$ observations was $36$. It was found later that an observation $48$ was wrongly taken as $23$. The corrected new mean is

$A$ cricketer scored some runs in his continuous $9$ innings. He scored $100$ runs in his $10^{th}$ innings and this increased his average by $8$ runs. What was the average of his runs at the end of $10^{th}$ innings?