Under isothermal conditions two soap bubbles of radii a and b coalesce to form a single bubble of radius c. If external pressure is P_o, the surface tension is equal to :

Two soap bubbles with radii "a" and "b" combine to form a single bubble with radius "c" when the temperature is isothermal.
If the internal pressure of bubbles is P, then the outward pressure is $P_0$.

${\mathrm{P}}_{\mathrm{a}}=\left({\mathrm{P}}_0+\frac{4\mathrm{T}}{\mathrm{a}}\right), {\mathrm{P}}_{\mathrm{b}}=\left({\mathrm{P}}_0+\frac{4\mathrm{T}}{\mathrm{b}}\right),{\mathrm{P}}_{\mathrm{c}}=\left({\mathrm{P}}_0+\frac{4\mathrm{T}}{\mathrm{c}}\right)$

$\mathrm{volume}, {\mathrm{V}}_{\mathrm{a}}=\frac{4}{3}{\mathrm{\pi a}}^3,{\mathrm{V}}_{\mathrm{b}}=\frac{4}{3}{\mathrm{\pi b}}^3,{\mathrm{V}}_{\mathrm{c}}=\frac{4}{3}{\mathrm{\pi c}}^3$

as mass is conserved,

${\mathrm{\mu }}_{\mathrm{a}}+{\mathrm{\mu }}_{\mathrm{b}}+{\mathrm{\mu }}_{\mathrm{c}}=\frac{{\mathrm{P}}_{\mathrm{a}}{\mathrm{V}}_{\mathrm{a}}}{{\mathrm{RT}}_{\mathrm{a}}}+\frac{{\mathrm{P}}_{\mathrm{b}}{\mathrm{V}}_{\mathrm{b}}}{{\mathrm{RT}}_{\mathrm{b}}}+\frac{{\mathrm{P}}_{\mathrm{c}}{\mathrm{V}}_{\mathrm{c}}}{{\mathrm{RT}}_{\mathrm{c}}}$

${\mathrm{P}}_{\mathrm{a}}{\mathrm{V}}_{\mathrm{a}}+{\mathrm{P}}_{\mathrm{b}}{\mathrm{V}}_{\mathrm{b}}+={\mathrm{P}}_{\mathrm{c}}{\mathrm{V}}_{\mathrm{c}}\mathrm{\_\_\_\_\_}\left(1\right)$

Substituting the value of pressure and volume,

$\left[{\mathrm{P}}_0+\frac{4\mathrm{T}}{\mathrm{a}}\right]\left[\frac{4}{3}{\mathrm{\pi a}}^3\right]+\left[{\mathrm{P}}_0+\frac{4\mathrm{T}}{\mathrm{b}}\right]\left[\frac{4}{3}{\mathrm{\pi b}}^3\right]=\left[{\mathrm{P}}_0+\frac{4\mathrm{T}}{\mathrm{c}}\right]\left[\frac{4}{3}{\mathrm{\pi c}}^3\right]$

$4\mathrm{T}({\mathrm{a}}^2+{\mathrm{b}}^2-{\mathrm{c}}^2)={\mathrm{P}}_0({\mathrm{c}}^3-{\mathrm{a}}^3-{\mathrm{b}}^3)$

$\mathrm{Surface} \mathrm{tension} \mathrm{T}=\frac{{\mathrm{P}}_0({\mathrm{c}}^3-{\mathrm{a}}^3-{\mathrm{b}}^3)}{4({\mathrm{a}}^2+{\mathrm{b}}^2-{\mathrm{c}}^2)}$

Hence the correct answer is $\mathrm{T}=\frac{{\mathrm{P}}_0({\mathrm{c}}^3-{\mathrm{a}}^3-{\mathrm{b}}^3)}{4({\mathrm{a}}^2+{\mathrm{b}}^2-{\mathrm{c}}^2)}.$