Problem Statement:
A train moving at a cover a rate of 90 kmph. Crosses a tunnel in 36 seconds. and other train which is 100 metres shorter moving at a cover a rate of 45 kmph. How much time will it take to go through the tunnel?

Solution:
To solve this problem, we need to first find the length of the tunnel. Let's assume that the length of the tunnel is 'x' meters.

Step 1: Find the speed of the first train in meters per second.
Given, the speed of the first train = 90 kmph
Converting kmph to m/s, we get:
90 kmph = (90*1000)/3600 m/s = 25 m/s

Step 2: Find the length of the first train in meters.
We know that the first train crosses the tunnel in 36 seconds. Therefore, the distance covered by the first train in 36 seconds is equal to the length of the tunnel plus the length of the train. Mathematically, we can write:
Distance covered by the first train in 36 seconds = x + length of the first train
We can also write:
Distance = Speed * Time
Therefore, we have:
x + length of the first train = 25 * 36
x + length of the first train = 900
As we don't know the length of the first train, we cannot solve for 'x' at this point.

Step 3: Find the speed of the second train in meters per second.
Given, the speed of the second train = 45 kmph
Converting kmph to m/s, we get:
45 kmph = (45*1000)/3600 m/s = 12.5 m/s

Step 4: Find the length of the second train in meters.
We know that the second train is 100 meters shorter than the first train. Therefore, the length of the second train can be written as:
Length of the second train = Length of the first train - 100 meters
Substituting this in Step 2, we get:
x + (length of the first train - 100) = 12.5 * t
where 't' is the time taken by the second train to cross the tunnel.

Step 5: Solve for 'x' and 't'.
We have two equations:
x + length of the first train = 900
x + (length of the first train - 100) = 12.5 * t
Subtracting the second equation from the first, we get:
100 = 12.5 * t
t = 8 seconds

Therefore, the time taken by the second train to go through the tunnel is 8 seconds.

Final Answer:
Option (B) 64 seconds.