A sample containing only caco3 and Mgco3 is ignited to CaO and Mgo . The mixture of oxides produced weight exactly half as much as the original sample .

Calculate the percentage of caco3 and mgco3 in the sample

molar mass CaCO3 = 40.1+12+3*16=100.1g
molar mass CaO= 40.1 +16=56.1
ratio molar weight CaO/CaCo3=56.1/100.1=0.56
molar weight MgCO3= 24.3+12+3*16=84.3
molar weight MgO=24.3+16=40.3
ratio 40.3/84.3=0.478

lets x proportion of salt Ca and 1-x that of Mg

0.56*x+(1-x) *0.478=0.5
0.56x+0.478-0.478x=0.5
0.082x=0.022
x=0.022/0.082=0.268

So 0.268=26.8%of CaCO3
0.732=73.2% of MgCO3