Explanation

Write p = kq, q = kr and r = ks (k ≠ 0) from the three given equalities. Then p³ + q³ + r³ = k³q³ + k³r³ + k³s³ = k³(q³ + r³ + s³), so the required ratio equals k³ exactly. Since p = k³s (applying the relations in chain), p/s = k³, which is option A. Note that r/q = k² and q/r = 1/k, so only p/s collapses the whole expression to k³.