Explanation:

- To determine the speed ratio of trains P and Q, consider the following:

- Both trains cross each other in 12 seconds.

- Combined length of trains = 120 + 120 = 240 meters.

- Relative speed = 240 meters / 12 seconds = 20 meters/second.

- Train P crosses a 240 meters long platform in 36 seconds:

- Total distance = length of train P + length of platform = 120 + 240 = 360 meters.

- Speed of P = 360 meters / 36 seconds = 10 meters/second.

- From the relative speed formula:

- Speed of Q = 20 meters/second (relative speed) - 10 meters/second (speed of P) = 10 meters/second.

- Speed ratio of P to Q = 10:10 = 1:1.

Correct Answer: Option 4 - 1:1