Explanation:
The given soap bubble is

Let \({P_1},{P_2}{\text{ }}\,\& \,{P_0}\) are the pressures shown in the figure
\({P_2} - {P_0} = \frac{{4T}}{{3\;cm}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\)
\({P_1} - {P_2} = \frac{{4T}}{{1\;cm}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(2)\)
From Eq's (1) & (2) we get
\({P_1} - {P_0} = 4T\left[ {\frac{1}{{3\;cm}} + \frac{1}{{1\;cm}}} \right] = \frac{{16T}}{{3\;cm}}\)
The radius of the single soap bubble that maintains the same pressure difference is
\(\frac{{16T}}{{3\;cm}} = \frac{{4T}}{r} \Rightarrow r = \frac{3}{4}\;cm\)