The sum of the digits of a two-digit number is $6$. If the digit at the unit's place is twice the digit at the ten's place,then that number is..........

Form the pair of linear equations for the following problem and find their solution by the substitution method.
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of $10 \, km$,the charge paid is ₹ $105$ and for a journey of $15 \, km$,the charge paid is ₹ $155$. What are the fixed charges and the charge per $km$? How much does a person have to pay for travelling a distance of $25 \, km$?

Solve by the method of substitution. Aftab tells his daughter,"Seven years ago,$I$ was seven times as old as you were then. Also,three years from now,$I$ shall be three times as old as you will be." Represent this situation algebraically.

Solve the following pair of linear equations by the substitution method.
$x+y=14$
$x-y=4$

Solve the following pair of linear equations by the substitution method.
$s-t=3$
$\frac{s}{3}+\frac{t}{2}=6$

Solve the following pair of linear equations by the substitution method:
$\frac{3x}{2} - \frac{5y}{3} = -2$
$\frac{x}{3} + \frac{y}{2} = \frac{13}{6}$