(i) To find the ratio of distances AB : BC, we use the equation of motion:

\(v^2 = u^2 + 2(-a)s\)

For AB: \(12^2 = 20^2 - 2a \times AB\)

\(144 = 400 - 2a \times AB\)

\(2a \times AB = 256\)

\(AB = \frac{128}{a}\)

For BC: \(6^2 = 12^2 - 2a \times BC\)

\(36 = 144 - 2a \times BC\)

\(2a \times BC = 108\)

\(BC = \frac{54}{a}\)

The ratio \(AB : BC = \frac{128/a}{54/a} = \frac{128}{54} = \frac{64}{27}\).

(ii) To find the distance BC, we first find the deceleration \(a\) using the entire distance AD:

\(0 = 20^2 - 2a \times 80\)

\(0 = 400 - 160a\)

\(a = 2.5\)

Now, substitute \(a\) back to find BC:

\(BC = \frac{54}{2.5} = 21.6 \text{ m}\).