The gravitational acceleration on the surface of planet A is:
[tex]g_A = \frac{GM_A}{r_A^2} [/tex]
where G is the gravitational constant, [tex]M_A[/tex] is the mass of planet A and [tex]r_A[/tex] its radius.
Similarly, the gravitational acceleration on the surface of planet B is:
[tex]g_B = \frac{GM_B}{r_B^2} [/tex]
The ratio between the gravitational acceleration on planet A and B becomes:
[tex] \frac{g_A}{g_B}= \frac{GM_A / r_A^2}{GM_B/r_B^2} = \frac{M_A r_B^2}{M_B r_A^2} [/tex]
The problem says that the two masses are equal: [tex]M_A = M_B[/tex] while planet A has 3 times the radius of planet B: [tex]r_A = 3 r_B[/tex]. Substituting into the ratio, we get:
[tex] \frac{g_A}{g_B} = \frac{M_B r_B^2}{M_B (3 r_B)^2} = \frac{1}{9} [/tex]
so, gravity on planet B is 9 times stronger than planet A.
