What is the ratio of dark pink balls to the dark green balls?

For Pink balls (12% of total):

Total pink balls = $0.12 \times 1000 = 120$ balls

Ratio of light:dark pink = $1:7$

Total parts of pink = $1 + 7 = 8$ parts

Dark pink balls = $\frac{7}{8} \times 120 = 105$ balls

For Green balls (18% of total):

Total green balls = $0.18 \times 1000 = 180$ balls

Ratio of light:dark green = $1:3$

Total parts of green = $1 + 3 = 4$ parts

Dark green balls = $\frac{3}{4} \times 180 = 135$ balls

Therefore, ratio of dark pink balls to dark green balls = $105:135$

Simplifying $105:135 = 7:9$