A number consists of two digits whose sum is 8. If 18 is added to the number, its digits are reversed, find the number?

Let us assume that one of the digit of the two digit number is X, then problem the other number will be (8 - X)

From problem we get that, if we add 27 to the number the digits get interchanged and also since the number is a two digit number then X will in tens place (7 - X) will be in ones place.

So the equation we get

10X + (8 - X) + 18 = 10(8 - X) + X

10X + 8 - X + 18 = 80 -10X + X

9X + 26 = 80 - 9X

9X + 9X = 80 - 26

18X = 54

X = 54/18

X = 3,

So the digit in tens place = 3 the digit in ones place is (8 - 3 = 5) , then the number is 35 and when 18 is added the result is 53, the digits interchange their position in the new number.

Ans: 35.