Question

The digits of a 2-digit number differ by 5. If the digits are interchanged and the resulting
number is added to the original number, we get99. Find the original number.

Answer 1

Answer:

Let the 2-digit number be 10x + y.

Given:

1) x-y = 5

2) (10y + x) + (10x + y) = 99

=> 11y + 11x = 99 .... ÷11

=> x + y = 9

Now simultaneously solve them (eliminating y here by adding both equations):

x+x + y-y = 9+5

=> 2x = 14

=> x = 7

So, y = 9-x

=> y = 2

Therefore, original number is 10x + y = 72

Hope it helps.

Edit: The question is correct, I did a mistake in calculations. Apologies for that.