If $2x + y = 35$ and $3x + 4y = 65$,then find $\frac{x}{y}$.

While arranging the students of standard $X$ in rows,if two rows are reduced,then one more student has to be arranged in each of the remaining rows. If three more rows are formed,then one student has to be taken off from each of the previously arranged rows. Find the total number of students in the class.

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.

By the method of substitution,solve the following pair of linear equations: $3x - 7y = 18, 6x - 14y = 12$.

Solve the following pair of linear equations in two variables using the graphical method: $2x + y = 7$ and $x - 2y = 6$.

$A$ passenger buys $5$ tickets for Ahmadabad to Nadiad and $10$ tickets for Ahmadabad to Vadodara for Rs. $1050$. The total cost of a ticket for Ahmadabad to Nadiad and a ticket for Ahmadabad to Vadodara is Rs. $130$. Find the cost of a ticket for Ahmadabad to Nadiad as well as the cost of a ticket for Ahmadabad to Vadodara.