Question

the sum of digits oftwo digit number is 13. if the number is subtracted from the one obtained by interchanging the digits the result is 45.what is the number​

Answer 1

Step-by-step explanation:

$\bf\underline{\underline{\red{Given:-}}}$

• The sum of digits of a two digit number is 13.

• If the number is subtracted from the one obtained by reversing the digits the result is 45.

$\bf\underline{\underline{\blue{To\: Find:-}}}$

• The original number.

$\bf\underline{\underline{\green{Solution:-}}}$

Let the tens digit of the number be x

And ones digit be y

Then:-

The original number = 10x + y

The number obtained by reversing the digits = 10y + x

Case 1:-

$\rm The\: sum \: of \: the \: digits\: is\: 13$

$\rm x + y = 13.......(i)$

Case 2:-

If the number is subtracted from the one obtained by reversing the digits the result is 45.

$\rm Reversed\: number - Original \: number = 45$

$\rm \implies 10y + x - ( 10x + y ) = 45$

$\rm \implies 10y + x - 10x - y = 45$

$\rm \implies 9y - 9x = 45$

Dividing the whole equation by 9

$\rm \implies \dfrac{9y}{9} - \dfrac{9x}{9} = \dfrac{45}{9}$

$\rm \implies y - x = 5......(ii)$

Adding equations (i) and (ii)

$\rm \implies x + y + y - x = 13 + 5$

$\rm \implies 2y = 18$

$\rm \implies y = \dfrac{18}{2}$

$\rm \implies y = 9$

Substituting y = 9 in equation (i)

$\rm \implies x + y = 13$

$\rm \implies x + 9 = 13$

$\rm \implies x = 13- 9$

$\rm \implies x = 4$

The original number = 10(x) + y

= 10(4) + 9

= 40 + 9

= 49

$\underline{\boxed{\purple{\rm \therefore The \: number = 49}}}$