10g of a mixture of ${CaCO}_3$ and ${Na}_2{CO}_3$ on ignition suffered a loss in weight of $2.2 g$. The mass ratio of ${CaCO}_3$ and ${Na}_2{CO}_3$ is

 According to question, reaction can be written as

${CaCO}_3+{Na}_2{CO}_3\stackrel{\Delta }{⟶}CaO+{CO}_2+{Na}_2{CO}_3$

Here ${Na}_2{CO}_3$ did not decompose since it is thermally very stable and hence ${CaCO}_3$ is the only one which burns and give out carbon dioxide. 

Now acc. to the reaction, 100g  gives 44g carbon dioxide

Hence using unitary method, 2.2g carbon dioxide can be produced by 5g ${CaCO}_3$

Thus masses of ${CaCO}_3$ and ${Na}_2{CO}_3$ 5g and 5g respectively

Thus Mass Ratio= Mass of ${Na}_2{CO}_3$/Mass of${CaCO}_3$

                             = 1:1

Hence option (A) is answer to the question.