Let the big integer be "a" and small integer be "b".
thus given a - b= 30

now we have the answer choices in the ratio form , we can use that ratio form to put in our original equation to check if we can get a valid value .
E.g. option A states 5:2 so let the ratio be x between them , thus a =5x and b=2x
and a - b = 30 --> 5x-2x=30 --> 3x=30 or x=10 , thus we get a valid ratio and the option choice is correct, in case we do not get an integer ratio we can deem that answer choice to be incorrect
Option B --> 7:3 i.e. a=7x and b =3x and 7x-3x=30 --> 4x= 30 , thus we will not get a valid ratio for our integers , option incorrect
Option C --> a=8x , b =5x , thus 8x-5x=30 --> 3x=10 , x=10 , valid , correct
Option D --> a = 9x , b =4x , thus 9x-4x=30 --> 5x=30 , x=6 , valid ratio , correct
Option E --> a = 11x, b = x, thus 11x-x=30 --> 10x=30 , x=3 , valid ratio , correct
Answers A,C,D,E

Take the difference of numerator and denominator in each option , 30 should be the multiple of the difference. Therefore, a,c,d,e is the answer