Question

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

Answer 1

$\huge\textbf{ANSWER}$
$<b>$
Given sum of digits of two digit number is 12 

Let the digits in ones place be x 

Therefore, 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

9x + 12 = 120 - 9x + 54

18x = 120 + 54 - 12

18x = 174 – 12

18x = 162 

∴ x = 9 

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

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