When 20ml of methane and 20ml of oxygen are exploded together and the reaction mixture is cooled to laboratory temperature. The resulting volume of the mixture

CH4 +2O2 -> CO2+ 2H2O

1mol of methane reacts with 2 moles of O2 to give 1mol of CO2.

By Gay Lussacs law
2vol of O2 react with 1vol of CH4


1ml of CH4 react with 2ml of O2 to give 1ml of CO2

10ml of CH4 react with 20ml of O2 to give 10ml of CO2

Vol. of CH4 left=10ml
Vol.of CO2 formed=10ml

Here water formed is in gaseous phase,so vaporises.

Therefore,
Total volume of mixture=20ml