Question

the sum of the digits of a two-digit number is 12 if new number is formed by reversing the digit is greater than original number by 54 find the original number

Answer 1

Given sum of the digits is 12

Let the digits in ones place be x

Hence the digit in tens place is (12 – x)

The original number = 10(12 – x) + x = 120 – 9x

Number formed by reversing the digits = 10x + (12 – x) = 9x + 12

Given that number formed by reversing the digits is 54 greater than the original number.

⇒ 9x + 12 = (120 – 9x) + 54 = 174 – 9x

⇒ 18x = 174 – 12 = 162

∴ x = 9

The original number = 120 – 9x = 120 – 9(9) = 39

Answer 2

$\textbf{Solution:}$

Let the number at one's place be x.

and ten's place be ( 12 - x ).

•°• Original number

=> 10(12-x) + x

=> 120 - 10x + x

=> 120 - 9x

the number obtained by interchanging the digits

=> 10x + 12 - x

=> 9x + 12

$\bold{\boxed{A.T.Q}}$

9x + 12 = 54 + 120 - 9x

=> 9x + 9x = 174 - 12

=> 18x = 162

=> x = 162/18 = 9

•°• original number

=> 120 - 9x

=> 120 - 9 × 9

=> 120 - 81

=> 39.

therefore the required number is 39.
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