In a match, average of runs scored by five players is $49.$ It the runs scored by four players are $75,30,$ $63$ and $21$ respectively, then how many runs did the fifth player score?

A student was asked to find the arithmetic mean of the numbers $3,11,7,9,15,13,8,19,17,21,14$ and $x$. He found the mean to be $12 .$ What should be the number in place of $x ?$

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 be $100,$ find the value of $x .$

The average temperature from Monday to Wednesday is $37^oC$ while the average temperature from tuesday to thursday is $34^{\circ} C$. The temperature of thursday is $\frac{4}{5}$ times to that of Monday. Find the temperature of thursday in $^{\circ} C$ ?

The mean of $100$ items was $46 .$ Later on, it was discovered that an item $16$ was misread as $61$ and another item $43$ was misread as $34.$ It was also found that the number of items was $90$ and not $100 .$ Then, what is the correct mean?