The cost of $5$ pants and $8$ shirts is ₹ $3100$. If the cost of a pant is ₹ $x$ and a shirt is ₹ $y$,then the linear equation in two variables is:

Solve the following pair of equations by reducing them to a pair of linear equations:
$\frac{1}{3x+y} + \frac{1}{3x-y} = \frac{3}{4}$
$\frac{1}{2(3x+y)} - \frac{1}{2(3x-y)} = -\frac{1}{8}$

The sum of the digits of a two-digit number is $13$. The number obtained by interchanging the digits is $9$ more than the original number. Find the original number.

$A$ boat goes $32 \, km$ upstream and $36 \, km$ downstream in $7$ hours. In $9$ hours,it can go $40 \, km$ upstream and $48 \, km$ downstream. Determine the speed of the stream and that of the boat in still water. (Speed of boat in still water is more than the speed of the stream of river.)

Solve the following pair of equations by the method of cross-multiplication:
$x + 2y + 1 = 0$
$2x - 3y - 12 = 0$

If $\frac{x+y}{x y}=2$ and $\frac{x-y}{x y}=6,$ then $x=\ldots \ldots \ldots \ldots .$