Seven times a two - digit number is equal to four times the number obtained by reversing the digits. If the difference between the digits is 3, the number is

Let the 2-digit number is $=10x+y$

The number obtained by reversing the digit $=10y+x$

From equation $\left(1\right)$

Given sever times of two – digit number is equal to four – times the number obtained by reversing the digits.

i.e. $7(10x+y)=4(10y+x)$

$\Rightarrow 70x+7y=40y+4x$

$66x-33y=0$

$2x-y=0\to \left(1\right)$

And difference between the digits is 3

i.e. $y-x=3\to \left(2\right)$

$\left(1\right)+\left(2\right)$

$\begin{array}{l}2x-y=0\\ \underset{\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_}{-x+y=3}\\ x=3\end{array}$

From (1) $2\left(3\right)-y=0$

$y=6$

$\therefore$ the two digit number is $=10x+y$

$=10\left(3\right)+6$

$=36$