The thermal decomposition of a group 2 nitrate would decompose according to:
M(NO3)2 (s) —-> MO (s) + 4NO2 (g) + O2 (g). This is the first thing you should write.
Then I would work out (1.53/3.00) x 100 = 51%. So 51% gas is produced by mass.
Then work out the atom economy of the general decomposition formula using each group 2 ion, and see which group 2 metal.
The Mr of Sr(NO3)2 is 211.6 and the Mr of 4NO2 + O2 = 216. So these Mr values will make the 49/51% Mr ratio we’re interested in.
Hence the answer is Strontium.
The most common way to answer the question is just simply trial and error, there are only several group 2 metals, so just substitute their different Mr values until you find the one that works.