A two digit number is equal to 21 times the difference of its digits. If 36 is…

For any two-digit number, if the tens digit is x and the units digit is y, the number equals 10x + y, and the number formed by reversing its digits equals 10y + x. Subtracting the reversed number from the original always gives 9 times the difference of the digits — this identity turns digit-reversal word problems into simple linear equations.

1. Let the tens digit be x and the units digit be y, so the original number = 10x + y.

2. The number equals 21 times the difference of its digits: 10x + y = 21(x - y). This simplifies to 22y = 11x, i.e., x = 2y.

3. Subtracting 36 reverses the digits: (10x + y) - 36 = 10y + x. This simplifies to 9(x - y) = 36, i.e., x - y = 4.

4. Substituting x = 2y into x - y = 4 gives y = 4, so x = 8.

5. The original number = 10x + y = 10(8) + 4 = 84.

Check both conditions with 84: the digits 8 and 4 differ by 4, and 21 times 4 equals 84, satisfying the first condition. Subtracting 36 gives 84 minus 36 equals 48, which is exactly 84 with its digits reversed, satisfying the second condition. Both conditions hold together only for 84.