10 mL of a gaseous hydrocarbon CxHy is exploded with 80 mL of O2 (excess) and the mixture is restored to the initial temperature and pressure, at…

For $\mathrm{C_xH_y}+(x+\tfrac y4)\mathrm{O_2}\to x\mathrm{CO_2}+\tfrac y2\mathrm{H_2O(l)}$, the gas volume change per mole of hydrocarbon is a contraction of $1+\tfrac y4$ (liquid water occupies no volume, and excess $\mathrm{O_2}$ cancels out). The $\mathrm{KOH}$ absorbs only $\mathrm{CO_2}$: $10x=40$, so $x=4$. The first contraction gives $10(1+\tfrac y4)=30$, so $y=8$. The hydrocarbon is $\mathrm{C_4H_8}$ (check: $10\ \mathrm{mL}$ needs $60\ \mathrm{mL}$ $\mathrm{O_2}$, so $80\ \mathrm{mL}$ is indeed in excess). Open-chain isomers of $\mathrm{C_4H_8}$ (one C=C): but-1-ene, $(Z)$-but-2-ene, $(E)$-but-2-ene and 2-methylpropene. The cyclic isomers (cyclobutane, methylcyclopropane) are excluded.