Question

sum of digits of a two digit number is 12. when we interchange the digits, it is found that the resulting new number is smaller than the original by 36 . what is the original number?​

Answer 1

Answer:

Hope it may help

Step-by-step explanation:

answer is pinned along

Answer 2

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

Given

$\bold{Sum \ of \ the \ digits} = 12$

$\implies x+y=12--(1)$

$\bold{Number \ obtained \ after \ interchanging \ digits \ is \ 36 \ less \ than \ the \ original \ number}$

$\implies 10y+x=10x+y-36\\\implies 10y+x-10x-y=-36\\\implies 9y-9x=-36\\\implies 9x-9y=36\\\implies x-y=4--(2)$

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

$x+y=12\\\underline{x-y=4}\\\underline{\underline{2x=16}}\\\implies x = 8\\\implies y = 4$

$\boxed{\boxed{\bold{Therefore, \ the \ required \ number \ is \ 84}}}}}}}}$