Question

The sum of the digits of a two digit number is 9.if the digits of the numbers are reversed the new number is decreased by 9.find the number

Answer 1

Let the digits are x and y.
the number will be 10x+y.

sum of digits = 9
x + y = 9 
x = 9-y

if digits are reversed, the new number will be 10y+x

(10x+y) - 9 = 10y+x
⇒ 10x + y - 9 - 10y - x = 0
⇒ 10x - x + y - 10y - 9 = 0
⇒ 9x - 9y - 9 = 0
⇒ 9(x - y - 1) = 0
⇒ x - y - 1 = 0
⇒ 9 - y - y - 1 = 0
⇒ -2y + 8 = 0
⇒ 2y = 8
⇒ y = 4
    x = 9-y = 9-4 = 5
The number is 10x+y = 10×5+4 = 54