Question

The sum of the digit of a 2 digit no is 12 if the new no formed by reversing the digit is greater then the original no by 54 find the original no

Answer 1

Step-by-step explanation:

Let the numbers of the two digit number be x and y.

Then the two digit number is 10x+y.

It is given that x + y = 12 ……….(1)

It is also given that the new number formed by reversing the digits is greater than the original number by 54.

So,

10y + x –(10x + y) = 54

⇒ 9y – 9x = 54

⇒ y – x = 6………..(2)

On adding equation (1) and (2) we get,

⇒ x + y + y – x = 18

⇒ 2y = 18

⇒ y = 9

putting the value of y in equation (1) we get,

⇒ x + 9 = 12

⇒ x = 3

We have assumed the number is 10x +y.

On putting the value of x and y we get 10(3) + 9 =39.

Hence the number is 39.