A number $P$ is greater than $Q$ by $60\%$ and greater than $R$ by $30\%$. What is the ratio of $Q$ and $R$?

Let's express $Q$ and $R$ in terms of $P$:
1. $P$ is greater than $Q$ by $60\%$:

$$P=Q+0.60Q=1.6Q⟹Q=\frac{P}{1.6}$$

2. $P$ is greater than $R$ by $30\%$:

$$P=R+0.30R=1.3R⟹R=\frac{P}{1.3}$$

Now, find the ratio of $Q$ and $R$ ($\frac{Q}{R}$):

$$\frac{Q}{R}=\frac{\frac{P}{1.6}}{\frac{P}{1.3}}=\frac{1.3}{1.6}=\frac{13}{16}$$

Thus, the ratio $Q:R$ is equal to $13:16$.