First of all, at the same temperature and pressure, same moles of any gas occupies the same volume. In another word, the question becomes 15 parts of the mixture gave 20 parts of CO2.
1 part of C2H4 gives 2 parts of CO2, and 1 part of CH4 gives 1 part of CO2. Since the mixture gave 20-15 = 5 parts more CO2 than, these 5 parts must be generated from C2H4. Therefore CH4 was 15-5 = 10 parts, C2H4 was 5 parts. So the original mixture contained 10 mL of C2H4 and 5 mL of CH4.