The ratio of velocity of hour's hand and minute's hand of a clock is

Let us consider one complete rotation ($360^{\circ }$) of a hand.
The minute's hand completes one full rotation in $1\text{hour}=60\text{minutes}$.
The hour's hand completes one full rotation in $12\text{hours}=12\times 60\text{minutes}=720\text{minutes}$.

Therefore, the ratio of their angular velocities is:

$$\frac{\text{Velocity of hour’s hand}}{\text{Velocity of minute’s hand}}=\frac{\frac{360^{\circ }}{720}}{\frac{360^{\circ }}{60}}=\frac{60}{720}=\frac{1}{12}$$

Hence, the ratio is $1:12$.