$10$ $years$ ago the average age of all the $25$ $teachers$ of the Girls college was $45\, years.$ $4 \,years$ ago, the principal has retired from her post at the age of $60 \,year.$ So after one year a new principal whose age was $54 \,years$ recruited from outside. The present average age of all the teachers is, if principal is also considered as a teacher
$54 \frac{18}{25}$ years
$55 \frac{17}{25}$ years
$49 \frac{1}{2}$ years
$49 \frac{2}{3}$ years
A student finds the average of ten $2 -$digit numbers. While copying numbers, by mistake, he writes one number with its digits interchaged. As a result his answer is $1.8$ less than the correct answer. The diference of the digits of the number, in which he made mistake, is
The average of $X_{1}, X_{2}$ and $X_{3}$ is $14 .$ Twice the sum of $X_{2}$ and $X_{3}$ is $30 .$ What is the value of $X_{1} ?$
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
The average weight of $10$ students is increased by half a $kg$ when one of the students weighing $50\, kg$ is replaced by a new student. Find out the weight of the new student.(in $kg$)
If the average of $x$ and $\frac{1}{x}(x \neq 0)$ is $M,$ then the average of $x^{2}$ and $\frac{1}{x^{2}}$ is