$A$ train covered a certain distance at a uniform speed. If the train would have been $10\, km/h$ faster,it would have taken $2\, hours$ less than the scheduled time. And,if the train were slower by $10\, km/h$,it would have taken $3\, hours$ more than the scheduled time. Find the distance covered by the train. (in $, km$)

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method.
The area of a rectangle gets reduced by $9$ square units,if its length is reduced by $5$ units and breadth is increased by $3$ units. If we increase the length by $3$ units and the breadth by $2$ units,the area increases by $67$ square units. Find the dimensions of the rectangle.

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

Half the perimeter of a rectangular garden,whose length is $4\, m$ more than its width,is $36\, m$. Find the dimensions of the garden.

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method. $A$ fraction becomes $\frac{1}{3}$ when $1$ is subtracted from the numerator and it becomes $\frac{1}{4}$ when $8$ is added to its denominator. Find the fraction.

Check graphically whether the pair of equations
$x+3y=6$ $...(1)$
and $2x-3y=12$ $...(2)$
is consistent. If so,solve them graphically.