Correct Answer  Option 1 : 2 : 1
The correct answer is option 1) i.e. 2 : 1
CONCEPT:

Law of Universal Gravitation: It states that all objects attract each other with a force that is proportional to the masses of two objects and inversely proportional to the square of the distance that separates their centres.
It is given mathematically as follows:
\(F = \frac{Gm_1m_2}{R^2}\)
Where m1 and m2 are the mass of two objects, G is the gravitational constant and R is the distance between their centres.
 From the Law of Universal Gravitation, the gravitational force acting on an object of mass m placed on the surface of Earth is:
\(F = \frac{GMm}{R^2}\)
Where R is the radius of the earth.
From Newton's second law, F = ma = mg
\(⇒ mg =\frac{GMm}{R^2}\)
⇒ Acceleration due to gravity, \(g =\frac{GM}{R^2}\)
EXPLANATION:
Using \(g =\frac{GM}{R^2}\)
Acceleration due to gravity on Earth, \(g_e =\frac{GM_e}{R_e^2}\)
Acceleration due to gravity on Saturn, \(g_s =\frac{GM_s}{R_s^2}\)
Given that:
R_{s} = 2R_{e} and M_{s} = 2M_{e}
\(\Rightarrow g_s =\frac{G(2M_e)}{(2R_e)^2}\)
Ratio = \(\frac{g_e}{g_s} =\frac{\frac{GM_e}{R_e^2}}{\frac{G2M_e}{(2R_e)^2}}\)
\(\Rightarrow \frac{g_e}{g_s} = \frac{(2R_e)^2}{2} \times \frac{1}{R_e^2}\)
\(\Rightarrow \frac{g_e}{g_s} = \frac{4}{2}=\frac{2}{1}\)