The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 18. Find the number.

Let unit and tens digit be x and y. 

∴ Original number = 1x + 10y …(i) 

Reversed number = 10x + 1y 

According to question, 

x + y = 8 

⇒ y = 8 – x …(ii) 

Also, 1x + 10Oy – (10x + y) = 18 

⇒ x + 10y – 10x – y = 18 

⇒ 9y – 9x = 18 

⇒ y – x = 2 …[Dividing both sides by 9] —-(iii) 

⇒ 8 – x – x = 2 …[From (iii)] 

⇒ 8 – 2 = 2x 

⇒ 2x = 6 

From (it), y = 8 – 3 = 5 

From (i), Original number = 3 + 10(5) = 53