The sum of the digits of a two-digit number is 6. When the digits are reversed, the number decreases by 18. Find the original number.

The number is 42

Explanation:

Let the digits be a and b.

The sum of the digits of a two-digit number is 6

That is

a + b = 6

When the digits are reversed, the number decreases by 18

ab - ba = 18

We need to find the number

Since ab - ba = 18, we know that a is greater than b.

Take a = 4

4 + b = 6

b = 6 - 4 = 2

That is the number is ab = 42

When it is reversed the number is 24.

42 - 24 = 18, hence correct

The number is 42