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 $Rs.$).

Which of the following is a solution of the linear equation in two variables $x - 2y = 4$?

Solve the following pair of linear equations by the elimination method and the substitution method:
$\frac{x}{2} + \frac{2y}{3} = -1$ and $x - \frac{y}{3} = 3$

Five years ago,the sum of the ages of a father and two sons was $x$ years. Then,after five years,the sum of the ages of all will be $\ldots \ldots \ldots$ years.

$A$ 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 $Rs.$).

On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}}$ and $\frac{c_{1}}{c_{2}}$,find out whether the following pair of linear equations are consistent or inconsistent:
$\frac{4}{3} x + 2 y = 8$; $2 x + 3 y = 12$