Dear student,
Between sodium carbonate and sodium bicarbonate, only sodium bicarbonate decomposes to give sodium carbonate, CO2 and H2O. The gaseous products (CO2 and H2O) escape out into the atmosphere. Therefore an apparent loss in weight occurs during the reaction. This loss in weight corresponds to the amount of gaseous products formed. From the mass of gaseous products formed, the amount of sodium bicarbonate in the mixture can be obtained and thus the composition of the mixture can be found out.
Regards