Two freight trains, X and Y, of length 360 m and (360 + x) m respectively, are moving at the same constant speed. If train X and train Y pass a signal pole in 12 seconds and 18 seconds respectively, in what time will train Y cross a 450 m long bridge?

The correct answer is 33 sec.

Step 1: Find the speed of the trains
Let the constant speed of both trains X and Y be $v$.
Train X of length 360 m passes a signal pole in 12 seconds.
When a train passes a signal pole, the distance covered is equal to the length of the train.

$\text{Speed}=\frac{\text{Length of Train X}}{\text{Time taken}}$

$v=\frac{360\text{m}}{12\text{s}}=30\text{m/s}$

Step 2: Find the length of train Y
Train Y of length $(360+x)$ m passes a signal pole in 18 seconds at the speed of 30 m/s.
Distance covered by train Y to pass the signal pole = Length of train Y.

$\text{Length of Train Y}=\text{Speed}\times \text{Time}$

$\text{Length of Train Y}=30\text{m/s}\times 18\text{s}=540\text{m}$

Step 3: Calculate the time taken by train Y to cross a 450 m long bridge
When train Y crosses a bridge, the total distance to be covered is equal to the sum of the length of train Y and the length of the bridge.

$\text{Total Distance}=\text{Length of Train Y}+\text{Length of Bridge}$

$\text{Total Distance}=540\text{m}+450\text{m}=990\text{m}$

Now, calculate the time taken by train Y to cover this distance at a speed of 30 m/s:

$\text{Time}=\frac{\text{Total Distance}}{\text{Speed of Train Y}}$

$\text{Time}=\frac{990\text{m}}{30\text{m/s}}=33\text{sec}$

Thus, train Y will cross the bridge in 33 seconds.