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.

meritnation expert please answer to this qusstion as i am having my exams on sunday pls

Let the digit at one's place = *x*

digit at ten's place = 12 - *x*

Original number = 10(12 - *x*) + *x* = 120 - 9*x*

When the digits are reversed, then new number = 10*x* + (12 - *x*) = 9*x* + 12

According to the given condition,

9*x* + 12 = 120 - 9*x + *54

⇒ 18*x = *162 ⇒ *x =* 162 / 18 = **9**

so, original number = 120 - 9 × **9 = **120 - 81 = 39

So, the answer is **39**

**
**