If $2P=3Q=4R=5S$, then find $P:Q:R:S$.

Given the equality:
$$2P=3Q=4R=5S$$
To find the ratio $P:Q:R:S$, we find the Least Common Multiple (LCM) of the coefficients $2,3,4,$ and $5$:
$$\text{LCM}(2,3,4,5)=60$$
Now, divide each term by the LCM ($60$):
$$\frac{2P}{60}=\frac{3Q}{60}=\frac{4R}{60}=\frac{5S}{60}$$
$$\frac{P}{30}=\frac{Q}{20}=\frac{R}{15}=\frac{S}{12}$$
Hence, the ratio is:
$$P:Q:R:S=30:20:15:12$$