Let the digit on one’s place be y and the digit in ten’s place be x ∴ The number is = 10x + y Sum of the digits is 10 ∴ x + y = 10 Now, when 18 is added, the digits are reversed ∴ New number = 10y + x ∴ (10x + y) + 18 = 10y + x ⇒ 9x + 18 = 9y ⇒ x + 2 = y ∴ x + y = 10 ⇒ x + (x + 2) = 10 ⇒ 2x + 2 = 10 ⇒ 2x = 8 ⇒ x = 4 ∴ y = 10 – x = 10 – 4 = 6 ∴ The number is 10x + y = (10 × 4) + 6 = 46