Step 1: Write the molecular formulae of the acids.
Peroxysulphuric acid (also known as Caro's acid) has the molecular formula: \[ \mathrm{H_2S_2O_8} \] It contains 8 oxygen atoms. Pyrosulphuric acid (also known as oleum) has the molecular formula: \[ \mathrm{H_2S_2O_7} \] It contains 7 oxygen atoms.
Step 2: Add the total number of oxygen atoms.
\[ 8 \text{ (from } \mathrm{H_2S_2O_8}) + 7 \text{ (from } \mathrm{H_2S_2O_7}) = 15 \]