The Law of Multiple Proportions states that when two elements form more than one compound, the masses of one element that combine with a fixed mass of the other element are in a simple whole-number ratio. The first oxide has 57.1% oxygen and 42.9% carbon. For a fixed mass of carbon (42.9 parts), the oxygen is 57.1 parts. In the second oxide (carbon dioxide, (\text{CO}_2)), the ratio is C:O (= 12:32 = 3:8), so oxygen (= 8/(3+8) \times 100 = 72.7%). The ratio of oxygen in the two oxides for the same amount of carbon: (57.1:72.7 \approx 4:5.09), which is not exactly 1:2 but illustrates the principle. More precisely, the first oxide is CO (carbon monoxide: (12:16), oxygen = (16/28 \times 100 = 57.1%)) and the second is (\text{CO}2) (oxygen (= 32/44 \times 100 = 72.7%)); the ratio of oxygen for fixed carbon (= 16:32 = 1:2). Option 40.0% corresponds to no common binary oxide of carbon. Option 50.0% would require equal masses of C and O, inconsistent with known oxides. Option 66.7% would be an oxide (\text{CO}{1.5}), which is non-integer and unrealistic. NCERT covers the Law of Multiple Proportions with CO and (\text{CO}_2) as the canonical example. Plausibility check: (\text{CO}_2) contains (32/44 \times 100 = 72.7%) oxygen by mass, matching the correct option.