Correct Answer: 150 seconds

Solution : When two trains cross each other running in opposite directions, their relative speed is the sum of their speeds.
Given that train P crosses train Q in 45 seconds, the total length they cover is the sum of their lengths i.e. 1200 m + 1500 m = 2700 m.
Relative speed = $\frac{\text{Total Distance}}{\text{Time}}$ = $\frac{2700}{45}$ = 60 m/s
We know that the speed of train Q is 144 km/hr = 144 $\times \frac{5}{18}$  = 40 m/s.
The speed of train P is the relative speed minus the speed of train Q,
Speed of P = Relative speed – Speed of Q = 60 – 40 = 20  m/s
Now, if train P has to cross an 1800 metres long platform,
$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$
Time = $\frac{\text{Distance}}{\text{Speed}}$ = $\frac{1800+1200}{20}$ = 150 seconds
Hence, the correct answer is 150 seconds.