Solve the following pairs of equations by the method of elimination:
$x + 3y - 6 = 0$
$2x - y = 5$

$A$ railway half ticket costs half the full fare,but the reservation charges are the same on a half ticket as on a full ticket. One reserved first class ticket from station $A$ to $B$ costs $Rs. 2530$. Also,one reserved first class ticket and one reserved first class half ticket from $A$ to $B$ costs $Rs. 3810$. Find the full first class fare from station $A$ to $B$,and also the reservation charges for a ticket (in $Rs.$).

Solve the following pair of linear equations: $x+y=5xy$ and $3x+2y=13xy$.

If in a rectangle,the length is increased and breadth reduced each by $2$ units,the area is reduced by $28$ square units. If,however,the length is reduced by $1$ unit and the breadth increased by $2$ units,the area increases by $33$ square units. Find the area of the rectangle.

The sum of a two-digit number and the number obtained by interchanging its digits is $110$. If the number obtained by subtracting $10$ from the original number exceeds five times the sum of the digits of the original number by $4$,then find the original number.

The cost of $4$ pens and $4$ pencil boxes is $Rs.\, 100$. Three times the cost of a pen is $Rs.\, 15$ more than the cost of a pencil box. Form the pair of linear equations for the above situation. Find the cost of a pen and a pencil box (in $Rs.$).