The gravitational force exerted on the moon by the planet when the moon is at maximum distance 
is
where G is the gravitational constant, M and m are the planet and moon masses, respectively. This is the minimum force, because the planet and the moon are at maximum distance.
Similary, the gravitational force at minimum distance is
And this is the maximum force, since the distance between planet and moon is minimum.
The problem says that
exceeds 
by 11%. We can rewrite this as
Substituing the formulas of Fmin and Fmax, this equation translates into
and so, the ratio between the maximum and the minimum distance is
where G is the gravitational constant, M and m are the planet and moon masses, respectively. This is the minimum force, because the planet and the moon are at maximum distance.
Similary, the gravitational force at minimum distance is
And this is the maximum force, since the distance between planet and moon is minimum.
The problem says that
Substituing the formulas of Fmin and Fmax, this equation translates into
and so, the ratio between the maximum and the minimum distance is
