In a competitive examination,the average marks obtained was $45$. It was later discovered that there was some error in computerization and the marks of $90$ candidates had to be changed from $80$ to $50$,and the average came down to $40$ marks. The total number of candidates appeared in the examination 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?

The average of $6$ numbers is $20$. If one number is removed, the average becomes $15$. What is the number removed?

The average age of a board of directors of a company,having $10$ directors,was $48$ years. Coincidentally,when a director aged $53$ resigned from the board,another director died on the same day. $A$ new director aged $34$ joined the board. Next year in the same month,the average age of all the $9$ directors was found to be $46$ years. The age of the late (i.e.,dead) director at the time of his death was (in years):

The average age of $6$ members of a family is $20$ years. If the age of a servant is included,the average age increases by $25\%$. What is the age (in years) of the servant?

The average age of students of a class is $15.8 \, \text{years}$. The average age of boys in the class is $16.4 \, \text{years}$ and that of the girls is $15.4 \, \text{years}$. The ratio of the number of boys to the number of girls in the class is: