A two-digit number is such that the sum of the digits is 8. When 54 is added to the number, then the digits are reversed. The number is:

Question: A two-digit number is such that the sum of the digits is 8. When 54 is added to the number, then the digits are reversed. The number is:

Solution:
Let the ten's and unit digit be x and 8 - x
∴ The number be 10x + 8 - x = 9x + 8

ATQ,
9x + 8 + 54 = 10(8 - x) + x
⇒ 9x + 62 = 80 - 10x + x
⇒ 9x + 62 = 80 - 9x
⇒ 18x = 80 - 62
⇒ 18x = 18
∴ x = 1

∴ The number is 9 × 1 + 8 = 9 + 8 = 17