It is 3:2 I feel because on adding all the ratios only 3:2 results in 5 i.e 3+2=5 and 5 is not a factor of 12

Or

Here your first option is 2:1

Now splitting 12 in the Ratio 2:1 we get 8 and 4. So, it is possible.

Next you have 3:1 this is also possible ratio as it can be 9 and 3.

Now if we look at 3:2 then it is obviously not possible to split 12 into ratio of 3 and 2.

But still for last one we have7:5 this makes a total of 12. So 7 broken and 5 unbroken is also possible.

So, the correct answer is 3:2.