The sum of the digits of a two-digit number is 8. If the digits are reversed, the number is decreased by 54. What is the number?

Question: The sum of the digits of a two-digit number is 8. If the digits are reversed, the number is decreased by 54. What is the number?

Solution:
Let the two-digit number be 10x + y, where x = tens digit and y = ones digit.

Given,
1st condition: x + y = 8
⇒ x = 8 - y .......(1)

2nd condition:
(10x + y) - (10y + x) = 54
⇒ 9x - 9y = 54
⇒ 9(8 - y) - 9y = 54
⇒ 72 - 9y - 9y = 54
⇒ 72 - 18y = 54
⇒ - 18y = 54 - 72
⇒ - 18y = - 18
⇒ y = 1

From equation (1) we get,
x = 8 - y = 8 - 1 = 7

So the number is:
10x + y = 10(7) + 1 = 71