The sum of the digits of a two-digit number is 8. If 18 is added to the value of the number,

its digits get reversed. Find the number.

Let the two digit number be xy (i.e., tens digit is x, ones digit is y)

Its value can be expressed as 10x+y.

Given, x+y = 8 which gives y = 8 − x

Therefore its value is 10x+y

= 10x + 8 − x

= 9x + 8.

The new number is yx with value is 10y + x

= 10(8 − x) + x

= 80 – 9x

Given, when 18 is added to the given number (xy) gives new number (yx)

(9x + 8) + 18 = 80 – 9x

This simplifies to 9x + 9x = 80 – 8 – 18

18x = 54

x = 3 ⇒ y = 8 – 3 = 5

The two digit number is xy = 10x+y ⇒ 10(3)+5 = 30+5 = 35

E