The average marks obtained by $180$ students in an examination is $50$. If the average marks of passed students is $80$ and the average marks of failed students is $40$,then what is the number of students who failed the examination?

The sum of three numbers is $98$. If the ratio between the first and second is $2:3$ and that between the second and the third is $5:8$,then the second number is

The average temperature of Monday,Tuesday,Wednesday and Thursday is $60^{\circ}$. The average temperature for Tuesday,Wednesday,Thursday and Friday is $63^{\circ}$. If the ratio of temperature for Monday and Friday is $21: 25,$ then what is the temperature of Friday? (in $^{\circ}$)

Three years ago,the average age of a family of $5$ members was $27 \, \text{years}$. The present average age is also $27 \, \text{years}$ after the inclusion of a child into the family. Find the age of the child in years.

The average age of $x$ and $y$ is $20$ years. If $z$ were to replace $x$,the average would be $19$ and if $z$ were to replace $y$,the average would be $21$. Find the ages of $x, y$ and $z$.

The average of $20$ numbers is $30$ and that of other $30$ numbers is $50$. What is the average of all the numbers?