To solve the problem, we need to find the length of the bridge, given that two trains start from stations P and Q in the ratio of 3:2 and cross each other in 30 seconds while traveling at different speeds. Let's break down the problem step-by-step:

Step 1: Determine the Lengths of the Trains

The lengths of the trains are in the ratio 3:2. If the length of the train from P is \(3x\) meters, then the length of the train from Q is \(2x\) meters.

Step 2: Calculate the Relative Speed

The trains run in opposite directions with speeds 54 km/h and 72 km/h. To find the relative speed, we add the speeds:

\(\text{Relative Speed} = 54 + 72 = 126 \, \text{km/h}\)

Convert this speed into meters per second:

\(\text{Relative Speed} = 126 \times \frac{1000}{3600} = 35 \, \text{m/s}\)

Step 3: Use the Crossing Time to Find Total Length

Since the trains cross each other in 30 seconds, the total combined length of the trains is covered in that time. Thus:

\((\text{Length of Train from P}) + (\text{Length of Train from Q}) = 35 \times 30 = 1050 \, \text{meters}\)

Substitute the lengths:

\(3x + 2x = 1050\)

\(5x = 1050\)

\(x = 210\)

The length of the train from P is \(3x = 630 \, \text{meters}\).

Step 4: Determine the Length of the Bridge

The length of the train from P is 630 meters and it crosses a bridge in 90 seconds. The speed of the train from P is 54 km/h, which needs conversion:

\(54 \times \frac{1000}{3600} = 15 \, \text{m/s}\)

Using the distance formula \( \text{Distance} = \text{Speed} \times \text{Time} \), the total distance covered while crossing the bridge is:

\(15 \times 90 = 1350 \, \text{meters}\)

The length of the bridge is:

\(\text{Length of Bridge} = 1350 - 630 = 720 \, \text{meters}\)

Conclusion: The length of the bridge is 720 meters.