Problems on Trains

When the train crosses a pole, it covers its own length. Taking 5 seconds means speed = length/5. The platform is 160m, which is 60% longer than the train, so the train is 100m. Speed = 100/5 = 20 m/s.

Train speed = 60 km/hr = 60 × 5/18 = 50/3 m/s. If train length is L, platform is 2L, total distance = 3L. Distance = Speed × Time, so 3L = (50/3) × 34.2 = 50 × 11.4 = 570m. Thus L = 190m and platform = 2L = 380m. The train must travel its own length plus the platform length to cross completely.

The second train's speed is 25 m/sec. When trains move in opposite directions, their relative speed is (v1 + v2). Total distance = 200 + 240 = 440 m. Time = 4.4 sec. So (75 + v2) = 440/4.4 = 100 m/sec. Therefore v2 = 25 m/sec.

Relative speed when moving in same direction = 70 - 4 = 66 km/hr. Convert to m/s: 66 × 1000/3600 ≈ 18.33 m/s. Time = distance/relative speed = 140/18.33 ≈ 7.64 seconds ≈ 8 seconds. Option B would be correct if speeds were subtracted incorrectly.

Train speed = 30 km/h = 30×(5/18) = 25/3 m/s. Time to pass man = 8 seconds. Relative speed (man walking towards train) = 30 + 6 = 36 km/h = 36×(5/18) = 10 m/s. Train length = 10 × 8 = 80 m. Time to cross platform = 24 seconds. Total distance = train length + platform length = 25/3 × 24 = 200 m. Platform length = 200 - 80 = 120 m.

Relative speed of train and man = (42 - 6) km/hr = 36 km/hr = 10 m/s. Time to pass = Distance / Relative speed = 180 m / 10 m/s = 18 seconds. The train is traveling faster than the man, so we subtract their speeds.

Total distance = train length + platform length = 175 + 35 = 210 m. Time = 12 sec. Speed = 210/12 = 17.5 m/s. Convert to km/hr: 17.5 × (18/5) = 63 km/hr.

Let length of A = L, so length of B = 2L. Speed of A = L/25. Speed of B = 2L/75 = L/37.5. Ratio A:B = (L/25):(L/37.5) = 37.5:25 = 3:2 after multiplying by 1.5. Or: (L/25) / (2L/75) = (L/25) × (75/2L) = 75/50 = 3/2.

Train A: length = 100 m, speed = 60 km/hr = 16.67 m/s. Train B: speed = 120 km/hr = 33.33 m/s, opposite direction. Relative speed = 16.67 + 33.33 = 50 m/s. Time = 10 seconds. Total distance = relative speed × time = 50 × 10 = 500 m. Length of train B = total distance - length of train A = 500 - 100 = 400 m. Option B is correct.

Let the speed of the second train be v km/hr. Since both trains have the same length L and are moving in the same direction, relative speed = (60 - v) km/hr = (60 - v) × 5/18 m/s. The first train catches the second and leaves it 120m behind, so total relative distance covered = L + L + 120 = 2L + 120 meters. Time = 18 seconds. Therefore: Distance = Relative Speed × Time. However, we have two unknowns (L and v) and only one equation. But wait - catching means starting together, then overtaking by 2L (lengths of both trains). If they start side-by-side and first train overtakes by 120m, then 2L + 120 = (60 - v) × 5/18 × 18. This still has L as unknown. The standard approach assumes the 'catch and leave behind 120m' means relative distance = 120m only (both start together). Then 120 = (60 - v) × 5/18 × 18, giving 60 - v = 24, so v = 36 km/hr.

Let train length = L meters and speed = v m/s. For bridge 1: L+300 = 21v. For bridge 2: L+240 = 18v. Subtracting: 60 = 3v, so v = 20 m/s = 20 × 18/5 = 72 km/hr. The answer is derived by solving the two simultaneous equations.

Speed = Distance/Time. The train length is 100m and it crosses a pole in 10 seconds, so speed = 100/10 = 10 m/s. Convert to km/hr: 10 × 18/5 = 36 km/hr.

When trains move in the same direction, relative speed = difference of speeds. Here: (75-48) = 27 km/h = 27 × (5/18) = 7.5 m/s. In 14 seconds, distance covered = 7.5 × 14 = 105 m, which is the faster train's length. Options A (86 m), C (185 m), and D (210 m) are incorrect calculations.

When trains move in opposite directions, their relative speed is the sum: 38 + 25 = 63 km/hr = 63 × 5/18 = 17.5 m/s. Total distance to cover = sum of lengths = 280 + 350 = 630 m. Time = Distance/Speed = 630/17.5 = 36 seconds.

When a train and a person move in opposite directions, their relative speed is the sum of their individual speeds. Here, relative speed = 58 km/hr + 8 km/hr = 66 km/hr = 66 × (5/18) m/s = 55/3 m/s. Time to cross the person = distance/speed = 165 ÷ (55/3) = 165 × 3/55 = 9 seconds.