Question

The difference between a 2-digit number and the number formed by reversing its digits is 45. If the sum
of the digits of the original number is 13, then find the number.​

Answer 1

Let the ten's digit and the one's digit be x and y respectively. (x > y)

Given

The difference between a 2-digit number and the number formed by reversing its digits is 45.

$10x+y-10y-x=45\\\implies 9x-9y=45\\\implies x-y=5--(1)$

The sum  of the digits of the original number is 13.

$\implies x+y=13--(2)$

Solving (1) and (2), we get,

$x-y=5\\\underline{x+y=13}\\\underline{\underline{2x=18}}\\\implies x = 9\\\implies y = 4$

$\boxed{\boxed{\bold{Therefore, \ the \ number \ is \ 94}}}}}}}}}$

                                                       

Answer 2

The answer is 94.

EXPLANATION:

Let the unit digit be x and tens digit be (13-x)

According to the question we get

[10(13-x)+x] - [10x + 13-x] = 45

If u solve further you will get

130-10x+x-9x+13 = 45

-18x = -72

x=4

two digit number will be 10(13-x) + x = 94