There were $35$ students in a hostel. If the number of students increases by $7 ,$ the expenses of the mess increase by $Rs.\,42$ per $day$ while the average expenditure per head diminishes by $Rs.\,1$ Find the actual expenditure of the mess. (in $Rs.$)
$480$
$420$
$520$
$460$
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.
What is the age of a class teacher?
$I.$ There are $11$ students in the class.
$II.$ The average age of the students and the teacher is $14$ years.
$III.$ The average age of the teacher and the students is $3$ years more than that of the students.
The average of three consecutive odd numbers is $52$ more than $\frac{1}{3}$$^{rd}$ of the largest of these numbers. What is the smallest of these numbers ?
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 of $25$ results is $20 .$ the average of first $12$ results is $15$ and that of the last $12$ results is $18 .$ Then, the $13^{ th}$ results is