There's a four digit number. The numbers are represented by the letters ABCD. No number is repeated twice. The number A (first number) is definitely not zero, thus making it a four digit number. Now if ABCD is multiplied by 2, the answer will be DCBA (so the numbers will be in opposite order). What are the four numbers? And how did you get the answer?

Suppose

2000A + 200B + 20C + 2D = 1000D + 100C + 10B + A

that is

1999A + 190 B = 998 D + 80 C

Call E = D - 2A. Then 998 D = 1996 A + 998 E. Hence

3A + 190B = 998 E + 80 C.

This implies E = 0 or 1.

If E = 0, A must be a multiple of 10: impossible

If E = 1, then D = 2A +1 < 10 ===> A < 5 and

3A +190B = 998 + 80 C

So 3A ends with an 8, and A = 6 which is impossible.