Option 1: 1 : 2

This option suggests that the ratio of A to B is 1:2. However, if 15% of A is double of 30% of B, then it means that A is greater than B. So, this option is incorrect.

Option 2: 2 : 1

This option suggests that the ratio of A to B is 2:1. Again, if 15% of A is double of 30% of B, then A is greater than B. Therefore, this option is incorrect.

Option 3: 1:4

This option suggests that the ratio of A to B is 1:4. However, if 15% of A is double of 30% of B, it means that A is greater than B. Therefore, this option is incorrect.

Option 4: 4:1

This option suggests that the ratio of A to B is 4:1. If 15% of A is double of 30% of B, then it implies that A is four times greater than B. Therefore, this option is correct.

Therefore, the correct answer is option 4, which states that the ratio of A to B is 4