Suppose P and Q are distinct two-digit numbers consisting of the same digits. Then P - Q is

Let the two digits of the numbers be x and y. Any two-digit number can be expressed in the form 10u + v, where u is the tens digit and v is the units digit. Since P and Q consist of the same digits but are distinct, we can represent them as:

• P = 10x + y
• Q = 10y + x

The difference between the two numbers is calculated as:

P - Q = (10x + y) - (10y + x)

P - Q = 9x - 9y = 9(x - y)

Since x and y are integers, the expression 9(x - y) is always a multiple of 9. Therefore, the difference P - Q must be divisible by 9. For instance, if P = 31 and Q = 13, then P - Q = 18, which is divisible by 9. If P = 52 and Q = 25, then P - Q = 27, which is also divisible by 9.