$A$ 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 $x$?

Out of seven given numbers,the average of the first four numbers is $4$ and that of the last four numbers is also $4$. If the average of all the seven numbers is $3,$ then the fourth number is?

$A$ 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?

$A$ cricketer had a certain average of runs for his $64$ innings. In his $65^{th}$ innings,he is bowled out for no score on his part. This brings down his average by $2$ runs. What is his new average of runs?

The average of runs scored by a cricketer in his $99$ innings is $99$. How many runs will he have to score in his $100^{\text{th}}$ innings so that his average of runs in $100$ innings may be $100$?

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.