the sum of the digits of a two digit number is 12. if the new number formed by reversing the digits is greater than the original number by 54, find the original number.check your solution

**Solution :**** **

Let the unit digit = x

Ten’s digit = 12 –x

Original number = 10( 12 –x ) + x

= 120 – 10x + x

**Original number = 120 – 9x**

**Reversing the digits :**

Unit digit = 12 – x

Ten’s digit = x

New number = 10x + 12 – x

**New number = 9x +12**

As new number is less than the original number by 54

9x +12 = 120 – 9x -54

9x +12 = 66 – 9x

9x + 9x = 66 -12

18 x = 54

X = 3

Original number = 120 – 9x

= 120 – 9(3)

= 120 – 27

**Original number = 93**