The sum of two numbers is $8$. If the smaller number is $y$,then the larger number $x = \ldots \ldots \ldots \ldots$

Kushan went to a bookseller's shop and purchased $2$ textbooks of Mathematics $IX$ and $3$ textbooks of Mathematics $X$ for Rs. $250$. His friend Rajan also bought $4$ textbooks of Mathematics $IX$ and $6$ textbooks of Mathematics $X$ of the same kind for Rs. $500$. Represent this situation as a pair of linear equations in two variables.

Determine,algebraically,the vertices of the triangle formed by the lines:
$3x - y = 3$
$2x - 3y = 2$
$x + 2y = 8$

The graph of the equation $\ldots \ldots \ldots \ldots$ is a line perpendicular to the $X$-axis.

The sum and difference of the reciprocals of the ages of a son and father are respectively $\frac{5}{40}$ and $\frac{3}{40}$. Represent this as a pair of linear equations in two variables,where $x$ is the age of the son and $y$ is the age of the father.

Jamila sold a table and a chair for $Rs.\, 1050,$ thereby making a profit of $10\%$ on the table and $25\%$ on the chair. If she had taken a profit of $25\%$ on the table and $10\%$ on the chair,she would have got $Rs.\, 1065.$ Find the cost price of each (in $Rs.$).