Find the missing numbers ($X$ and $Y$) in the series and find the value of $\frac{Y}{X}$:
10, 10, 20, X, 240, 1200, Y

Let's find the logic of the series by observing the ratios of consecutive numbers:
* $10\times 1=10$
* $10\times 2=20$
* $20\times 3=X⟹X=60$
* $60\times 4=240$
* $240\times 5=1200$
* $1200\times 6=Y⟹Y=7200$

Now, we need to find the value of $\frac{Y}{X}$:

$$\frac{Y}{X}=\frac{7200}{60}=120$$