Find out the Numbers

        The difference between two numbers is 54. They are composed of the same two digits reversed. What are the numbers?

Answer: 71 and 17, 82 and 28 and 93 and 39.

Suppose X be the digit in the unit’s place and Y be the digit in the ten’s place of the larger number.

Then the larger numbers is (10 Y + X).

And the smaller number is (10 X + Y).

And the difference between them is (10 Y + X) – (10 X + Y) = 54

Or Y – X = 6

We know that Y cannot be greater than 9 and X cannot be less than 1 and Y – X is exactly 6. Considering these conditions there are only three possibilities for Y and X namely the pairs 9 and 3, 8 and 2, and 7 and 1.