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Consider the reaction between Mg and HCl :
Mg(s) + 2HCl(g) → MgCl₂(aq) + H₂(g) ...... (*)
1 mole of H₂ gas occupies 24000 cm³ in RTP.
No. of moles of H₂ formed = (600 cm³) / (24000 cm³/mol) = 0.0250 mol
Mole ratio Mg : HCl : H₂ = 1 : 2 : 1
No. of moles of Mg = 0.025 mol
No. of moles of HCl used in reaction (*) = (0.0250 mol) × 2 = 0.0500 mol

Consider the reaction between MgO and HCl :
MgO(s) + 2HCl(aq) → MgCl₂(aq) + H₂O(l) ...... (#)
No. of moles of HCl used in reaction (#) = (0.0540 - 0.0500 ) mol = 0.0040 mol
Mole ratio MgO : HCl = 1 : 2
No. of moles of MgO = 0.0040 × (1/2) = 0.0020 mol

Molar mass of Mg = 24.3 g/mol
Mass of Mg = (24.3 g/mol) × (0.0500 mol) = 1.215 g
Molar mass of MgO = 24.3 + 16.0 = 40.3 g/mol
Mass of MgO = (40.3 g/mol) × (0.0040 mol) = 0.161 g
Percentage by mass of MgO = [0.161/(0.161 + 1.215)] × 100% = 11.7%