There is a two digit number. The sum of its digit is 12. If we reverse the digits the original one is 54 less than the reversed one. Find the number.

Let the ten’s digit = x

Then, unit’s digit = (12– x)

Number = 10x + (12– x)

= 12 + 9x

Number obtained by reversing the digits = 10(12– x) + x

= 120 – 10x + x

= 120 – 9x

If we reverse the digits the original one is 54 less than the reversed one. So,

(12 + 9x) = (120 – 9x)–54

18x = 120 – 54 – 12

18x = 54

x = 3

So, ten’s digit = 3 and unit digit = 12– 3 = 9

Hence the required number is 39.

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