Question

$8$ times a $2$ digit number is equal to $3$ times the number obtained by reversing the order of the digit. If the difference between digit is $5$ then find the number.

Answer 1

Let number $10x+y$
Reversing digits we get $10y+x$
Given $8(10x+y)=3(10y+x)$
$80x+8y=30y+3x$
$80x-3x+8y-30y=0$
$77x-22y=0$
$77x=22y$
$7x=2y\to 1$
Difference of digits$=5$
$y-x=5\to 2$

Multiply equation $2$ by $2$ we get

$2y-2x=10$

Substitute equation one

$2y=7x\to 1$
$2y-2x=10$
$7x-2x=10$
$5x=10$ Number$=27$
$x=2$
$y=7$