The key to understanding this problem is realizing that the volume of each gas is directly proportional to the number of moles of each gas.
When the hydrocarbon undergoes combustion, all of the carbon appears as CO2 in the products, so in this example we see that the number of carbon atoms in the hydrocarbon must be 2, because the volume of CO2 is twice that of the original hydrocarbon.
Likewise, all of the hydrogen appears as H2O in the products. This means that the volume of O2 required to carry out the combustion must be greater than the volume of CO2 produced (because some of the O2 is needed to produce H2O).
In this problem, however, the volume of O2 consumed (15 cm3) is less than the volume of CO2 produced, which cannot be the case if the hydrocarbon is composed only of carbon and hydrogen.
The most likely case is that the data in the problem are incorrect.
The balanced equation for combustion of hydrocarbon CxHy is
CxHy+(x+y4)O2↔xCO2+(y2)H2O
If the volume of O2 consumed were actually 35 cm3, then we would say that because the moles of O2 consumed is 3.5 times higher than the moles of hydrocarbon produced, and
3.5=x+y4
We already know that x=2 from the volume of CO2 produced. Therefore, y=6 and the formula of the hydrocarbon would have been C2H6.
