Explanation:

- Train P and train Q are running in opposite directions.

- Train P crosses train Q completely in 45 seconds.

- Combined lengths of train P and train Q is 1200 m + 1500 m = 2700 m.

- Speed of train Q = 144 km/h, which converts to 40 m/s (144 x 1000/3600).

- Relative speed when crossing = sum of both trains' speed.

- \(Relative \ speed = \frac{Total \ length}{Time} = \frac{2700}{45} = 60 \ m/s \).

- Speed of train P = 60 m/s (relative speed) - 40 m/s (speed of train Q) = 20 m/s.

- To cross an 1800-meter platform: Time = \(\frac{Length \ of \ Train \ P + Platform}{Speed \ of \ Train \ P}\).

- Total length = 1200 m + 1800 m = 3000 m.

- Time = \(\frac{3000}{20} = 150 \ seconds\).

- Correct Answer: Option 3 - 150 seconds

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