The pressure inside two soap bubbles is 1.01 and 1.02 atmosphers respectively. The ratio of their volumes is

$\left(\mathrm{atmospheric} \mathrm{pressure} ={10}^5 \mathrm{Pa}\right)$

We know that

$\mathrm{Excess} \mathrm{Pressure} =\frac{\mathrm{Surface} \mathrm{Tension}}{ \mathrm{Radius}}$

Gauge pressure, or the difference between absolute pressure and atmospheric pressure, is the excess  pressure in this instance.

Thus the ratio of gauge pressure is 1:2. accordingly ratio of the radii is 2:1.

$\mathrm{Volume}\propto {\mathrm{radius}}^3$

Thus the ratio of volume is 8:1.