Problems on Trains

Train speed 54 km/h = 15 m/s. Length = speed×time = 15×36 = 540m. New speed after 20% reduction = 15×0.8 = 12 m/s. Platform length = 180m. Total distance = 540+180 = 720m. Time = 720/12 = 60 seconds. None of the options (52, 48, 96, 72) match 60 seconds.

Relative speed in same direction = 64 - 4 = 60 km/hr = 60 × (5/18) = 50/3 m/s. Time = 800 / (50/3) = 48 seconds. Subtract speeds because both move in same direction.

Relative speed = 36 + 45 = 81 kmph = 81 × 5/18 = 22.5 m/s. Total distance covered in 20 seconds = 22.5 × 20 = 450 m. If one train is 200 m, the other train = 450 - 200 = 250 m.

The faster train must cover its own length at the relative speed when crossing a person in the slower train. Relative speed = 60 + 20 = 80 km/hr = 80×(5/18) = 200/9 m/s. Time = 36 seconds. Length = Speed × Time = (200/9) × 36 = 800 meters.

Speed = 60 km/hr = 16.67 m/s. Train length = 16.67 × 18 = 300 m. Time to cross platform = 54 s, so (train + platform) = 16.67 × 54 = 900 m. Platform = 900 - 300 = 600 m.

Using the formula for trains crossing and continuing: Speed of A/Speed of B = √(time taken by B/time taken by A) = √(3/12) = 1/2. So Speed of B = 2 × Speed of A = 2 × 60 = 120 km/hr. Option A (180 km/hr) incorrectly uses direct ratio without square root, while C (60 km/hr) assumes equal speeds.

When trains move in opposite directions, relative speed is the sum of individual speeds. Total distance = 330 + 150 = 480 m. Time = 45 seconds. Relative speed = 480/45 = 10.67 m/s = 38.4 km/hr. If one train's speed is 24 km/hr, the other train's speed = 38.4 - 24 = 14.4 km/hr. Option B is correct.

Let train length=L and speed=V. Passing platform: (L+84)/V=21. Passing man: L/V=9 → L=9V. Substitute: (9V+84)/V=21 → 9V+84=21V → 12V=84 → V=7 m/s. Convert to km/hr: 7×(18/5)=25.2 km/hr. Use relative distance concept.

When trains move in the same direction, relative speed is the difference: 80 - 70 = 10 km/hr = 25/9 m/s. Distance = speed × time = (25/9) × 36 = 100m. This is the fast train's length.

Total distance to cross the tunnel = train length + tunnel length = 150 + 100 = 250 meters. Time taken = 15 seconds. Speed = 250/15 = 50/3 m/s. Converting to km/hr: (50/3) × (18/5) = 60 km/hr. Options A (45) and B (48) underestimate the speed, while D (72) overestimates it.

Total distance to cross = train length + platform length = 175 + 125 = 300 meters. Speed = 45 km/hr = (45 × 1000)/3600 = 12.5 m/s. Time = Distance/Speed = 300/12.5 = 24 seconds.

When crossing in the same direction, subtract speeds: relative speed = 60 - 6 = 54 km/hr = 54 × 5/18 = 15 m/s. Time = distance/speed = 675/15 = 45 seconds. The train must cover its own length relative to the man. Key distractors: 42 seconds (uses 60 km/hr without subtracting man's speed), 48 seconds (incorrect unit conversion).

Relative speed = 50 + 30 = 80 km/hr. Distance = 800 km. Time to meet = 800/80 = 10 hours. Distance from X = speed of train from X × time = 50 × 10 = 500 km. Option D matches this. Options A, B, C are incorrect distances.

Total distance = 180 + 120 = 300 m. Time = 15 seconds. Relative speed = 300/15 = 20 m/s = 20 × (18/5) = 72 km/hr. Let v1 be first train's speed. Since trains move in opposite directions: v1 + 30 = 72, so v1 = 42 km/hr. Standard train problem: add speeds for opposite direction, convert m/s to km/hr by multiplying by 18/5.

Speed = 90 km/hr = 25 m/s. Distance covered in 36 seconds = 25 × 36 = 900 m. This distance equals train length + platform length. Since platform is triple the train's length, total distance = train + 3×train = 4×train. So train length = 900/4 = 225 m. Platform length = 3 × 225 = 675 m, confirming the claimed answer D.