2. The sum of the digits of a 2-digit number is 11. When the digits are reversed, the new number formed is 45 less than the original number. Find the number.

Question

<!--[if !supportLists]-->1.      <!--[endif]-->The sum of the digits of a 2-digit number is 11. When the digits are reversed, the new number formed is 45 less than the original number. Find the number.

 

Answer 1

Let the number be x and y.

Given, x+ y= 11 --------------------(1)

and 10x + y = 10y +x +45

or 9x - 9y = 45

or x -y =5  ----------------(2)

On adding eq (1) and (2) we get:

2x = 16 or x = 8

putting the value of x in eq(1) we get:

8 + y = 11

or y = 3

Therefore, the original number is 83.