Answer:
1089
Step-by-step explanation:
The original number is A0CD, We have that DC0A = 9 x A0CD.
If A =1, then D = 9 and we have:
9C01 = 9 x 10C9
In order for this expression to be true, the following must also be true:
(C x 9) + 8 must be divisible by 10, which means that C x 9 must end in a 2.
The only multiple of 9 (from 9 to 81) that ends in a 2 is 72.
72 = 9 x 8.
Therefore, C must be 8 and the original number is 1089. Multiply it by 9 to check the answer:
1089 x 9 = 9,081
Therefore, 1089 is correct.
