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

If $\frac{5}{x}+\frac{3}{y}=4$ and $\frac{3}{x}+\frac{5}{y}=2,$ then $\frac{1}{x}-\frac{1}{y}=\ldots \ldots \ldots \ldots .(x, y \neq 0)$

There are some $25$ paise coins and some $50$ paise coins in a bag. The total number of coins is $150$ and the amount in the bag is Rs. $55$. Find the number of coins of each value in the bag.

Formulate the following problems as a pair of equations, and hence find their solutions:
Ritu can row downstream $20\, km$ in $2\, hours,$ and upstream $4\, km$ in $2\, hours.$ Find her speed of rowing in still water and the speed of the current.

Which of the following pairs of linear equations has a unique solution,no solution,or infinitely many solutions? In case there is a unique solution,find it by using the cross-multiplication method.
$x - 3y - 7 = 0$
$3x - 3y - 15 = 0$

If the sum of two numbers is $15$ and the subtraction is $1,$ then the smaller number of these two numbers is.........