In a two-digit number,the digit at the unit's place is $(x+1)$ and the digit at the ten's place is $(x+2)$,then that number is $\ldots \ldots \ldots \ldots .$

In $\Delta ABC$,$m \angle A = x$,$m \angle B = 3x$,and $m \angle C = y$. If $3y - 5x = 30$,show that the triangle is right-angled and find the measures of all three angles.

If $7x - 9y = 25$ and $9x - 7y = 23$,then $x + y = \dots$

The length of a rectangle is one and a half times its breadth. If the perimeter of the rectangle is $100 \,cm$, find the length and the breadth of the rectangle.

$A$ 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 $, km$)

Solve $2x + 3y = 11$ and $2x - 4y = -24$ and hence find the value of $m$ for which $y = mx + 3$.