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Three coplanar forces $P, Q, R$ acting at a single point are in equilibrium.
Given that the angle between $P$ and $Q$ is $120^\circ$, and the angle between $Q$ and $R$ is $120^\circ$, the remaining angle between $R$ and $P$ is:
$360^\circ - (120^\circ + 120^\circ) = 120^\circ$

Applying Lami's theorem:
$\frac{P}{\sin 120^\circ} = \frac{Q}{\sin 120^\circ} = \frac{R}{\sin 120^\circ}$

Since the denominators are identical, we have:
$P = Q = R$

Therefore, the ratio of $Q$ to $R$ is:
$Q : R = 1 : 1$