There are some students in the two examination halls $A$ and $B$. To make the number of students equal in each hall, $10$ students are sent from $A$ to $B$ but, if $20$ students are sent from $B$ to $A$, the number of students in $A$ becomes double the number of students in $B$, then find the number of students in the both halls.

In a competitive examination, $1$ mark is awarded for each correct answer while $1/2$mark is deducted for every wrong answer. Jayanti answered $120$ questions and got $90$marks. How many questions did she answer correctly?

The angles of a cyclic quadrilateral $ABCD$ are $\angle A=(6x+10)°, \angle B=\left(5x\right)°, \angle C=(x+y)°$ and $\angle D=(3y-10)°$.

Find $x$ and $y$ and hence the values of the four angles.

Graphically, solve the following pair of equations

$2x+y=6$ and $2x-y+2=0$

Find the ratio of the area of the two triangle formed by the lines representing these equations with the X-axis and the lines with the Y-axis.

Determine graphically, the vertices of the triangle formed by the lines

$y=x, 3y=x$ and $x+y=8$

Draw the graph of the equations $x=3, x=5$ and $2x-y-4=0$. Also find the area of the quadrilateral formed by the lines and the X-axis.

Determine, algebraically, the vertices of the triangle formed by the lines

$3x-y=3$

$2x-3y=2$

and $x+2y=8$