Solution “X” contains Na₂CO₃ and NaHCO₃, 20 ml of X when titrated using methyl orange indicator consumed 60 ml of 0.1M HCl. In another experiment, 20 ml of X solution when titrated using phenolphthalein consumed 20 ml of 0.1 M HCl. The concentraions (in mol lit^–1) of Na₂CO₃ and NaHCO₃ in X are respectively .

When phenolphthalein indicator is used, sodium carbonate is titrated to sodium bicarbonate.
When methyl orange indicator is used, sodium carbonate is titrated to sodium bicarbonate and sodium bicarbonate is titrated to carbonic acid.
Hence, 20 ml 0.1 M HCl corresponds to sodium carbonate
Number of milli-moles of sodium carbonate present =20×0.1=2mmol
60 ml of 0.1 M HCl used for titration with methyl orange indicator corresponds to mixture of sodium carbonate and sodium bicarbonate out of which complete titration of sodium carbonate to carbonic acid will require 40 mL of 0.1 M HCl and the remaining 20 mL of 0.1 M HCl will correspond to the titration of sodium bicarbonate present in the original mixture. Number of millimoles of sodium bicarbonate present in the original mixture  =20×0.1=2mmol

$[{\mathrm{Na}}_2{\mathrm{CO}}_3 ]=\left[{\mathrm{NaHCO}}_3\right]=\frac{2}{20}=0.1\mathrm{M}$