Question

the sum of the digits of a two digit is 13. If the digits are interchanged, and the resulting number is added to the original number, we get 143. what is the original number ​

Answer 1

GIVEN:-

• Sum of the digits of two digit is 13

• Digits are interchanged and the resulting Number us added to original number.

• The Number formed is 143

TO FIND:-

• The Original Number.

SOLUTION:-

Let the ones place be x

So,

$\implies\rm{One's\:place = x}$

$\implies\rm{Ten's\:Place =(13-x)}$

$\implies\rm{Original\:Number= 10(13-x)+(x)}$

$\implies\rm{Original\:Number= 130-10x+x}$

$\implies\rm{Original\:Number=130-9x}$

Now,

Atq.

$\implies\rm{One's\:Place =(13-x)}$

$\implies\rm{Ten's\:Place = x}$

$\implies\rm{New\:Number=10(x)+13-x}$

$\implies\rm{New\:Number=10x+13-x}$

$\implies\rm{New\: Number= 9x+13}$.

Again,

Atq.

$\implies\sf{New\:Number+Original\:Number=144}$

$\implies\sf{(9x+13+130-9x)=143}$

$\implies\sf{13+130=143}$

$\implies\sf{143=143}$

Hence,

This true for all x making 13.

Let' s take a example

49 = 4+9=13

94= 9+14 = 13