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

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93 is right answer
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