Question

The sum of the digits of a 2-digit number is 13. If the number obtained by interchanging the digits exceeds the original number by 27,find the numbers.​

Answer 1

Step-by-step explanation:

Let the number be =(y×10)+x

but, x+y=13

⇒y=13−x

Now interchange digits; we gwt

(x×10)+y = Number + 27

(x×10)+y = (y×10)+x + 27

(x×10)+(13−x) = ((13−x)×10)+x+27

10x + 13 - x = 130 - 10x + x + 27

10x+13−x−130+10x−x−27=0

20x - 2x - 144 = 0

18x = 144

x=8

y=13 - 8 = 5

Number = y×10 + x

= 5×10 + 8

= 50 + 8

= 58