Two trains of lengths 150 m and 250 m run on parallel lines. When they run in the same direction, they take 20 seconds to cross each other and, when they run in the opposite direction, they take 5 seconds to cross each other. What is the speed of the two trains?

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Let the speeds of the two trains be x m/s and y m/s.

Lengths of trains are 150 m and 250 m.

When trains run in the same direction, relative speed = |x - y| m/s.
Time taken to cross each other = 20 seconds.
Distance to be covered to cross each other = sum of lengths = 150 + 250 = 400 m.

So, 400 / |x - y| = 20 => |x - y| = 400 / 20 = 20 m/s.

When trains run in opposite directions, relative speed = x + y m/s.
Time taken to cross each other = 5 seconds.
Distance to be covered = 400 m.

So, 400 / (x + y) = 5 => x + y = 400 / 5 = 80 m/s.

Now we have two equations:
1) x + y = 80
2) |x - y| = 20

Assuming x > y:

x - y = 20
x + y = 80

Adding both equations:
2x = 100 => x = 50 m/s

Substituting x = 50 in x + y = 80:
50 + y = 80 => y = 30 m/s

Convert speeds from m/s to km/h:
1 m/s = 18/5 km/h

x = 50 * 18/5 = 180 km/h
y = 30 * 18/5 = 108 km/h

Check options: 180 km/h and 108 km/h is option 3.

However, the answer given is option 1: 150 km/h and 105 km/h.

Let's re-examine calculations:

Check relative speed calculations:

Given times and lengths:
Same direction: time = 20 s, distance = 400 m
Opposite direction: time = 5 s, distance = 400 m

Relative speeds:
Same direction: (x - y) = 400 / 20 = 20 m/s
Opposite direction: (x + y) = 400 / 5 = 80 m/s

Solving:
x + y = 80
x - y = 20
Adding: 2x = 100 => x = 50 m/s
Then y = 30 m/s

Speeds in km/h:
x = 50 * 18/5 = 180 km/h
y = 30 * 18/5 = 108 km/h

So the correct answer is option 3: 180 km/h and 108 km/h.

Therefore, the answer is option 3.

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