Some two-digit number is given. If you swap the numbers in it and multiply by 4, and then subtract

Some two-digit number is given. If you swap the numbers in it and multiply by 4, and then subtract the original number, you get 72. Find the original two-digit number.

Let a two-digit number consist of the digits A and B.

Then the number can be written both as AB and as the sum 10A + B.

After rearranging the numbers in places, it will be written as BA.

The BA number can also be written as a sum: 10B + A.

Let’s multiply this number by 4 and subtract the original number from it:

4 (10B + A) – (10A + B) = 72;

40B + 4A – 10A – B = 72;

39B – 6A = 72;

13B – 2A = 24;

13B = 24 + 2A;

B must be an integer. This is possible only if A = 1. For all other values of A, a fractional value of B is obtained.

If A = 1, then B = 26/13 = 2.

Correct answer: 12.