Three metallic spherical shells (not concentric) of radii R, 2R and...

For isolated (not concentric) metallic spherical shells, the charge given to each shell resides entirely on its outer surface.

The surface charge density $\sigma$ of a spherical shell of radius $r$ and charge $Q$ is given by:
$\sigma = \dfrac{Q}{4\pi r^2}$

Given that the surface charge densities on the outer surfaces of the three shells are equal:
$\sigma_1 = \sigma_2 = \sigma_3$

Substituting the values of charges and radii for each shell:
$\dfrac{Q_1}{4\pi R^2} = \dfrac{Q_2}{4\pi (2R)^2} = \dfrac{Q_3}{4\pi (4R)^2}$

$\dfrac{Q_1}{R^2} = \dfrac{Q_2}{4R^2} = \dfrac{Q_3}{16R^2}$

Multiplying by $R^2$, we get the ratio of the charges:
$Q_1 : Q_2 : Q_3 = 1 : 4 : 16$

Answer: $1:4:16$