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LIC ADO · Quantitative Aptitude

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Core Concept

Read this first — the foundation of the topic

→Core Concept

Train problems involve calculating time taken by trains to cross objects like poles, platforms, bridges, or other trains. The key is understanding that trains have length, unlike point objects

💡Key Rules

When a train crosses a stationary object like a pole, it travels a distance equal to its own length. When crossing a platform or bridge, it travels its own length plus the length of the platform/bridge. For two trains, use relative speed concept

🔑Essential Formulas

Time = Distance/Speed Speed = Distance/Time Relative Speed (same direction) = |S1 - S2| Relative Speed (opposite direction) = S1 + S2 Speed conversion: km/hr to m/s multiply by 5/18, m/s to km/hr multiply by 18/5

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Exam Patterns

What examiners ask — read before attempting PYQs

💡Remember

72 km/hr = 20 m/s (this conversion appears frequently)

✏️Worked Example 1

1

Distance covered = Length of train = 120m

2

Time taken = 8 seconds

3

Speed = Distance/Time = 120/8 = 15 m/s

4

Convert to km/hr = 15 × 18/5 = 54 km/hr Answer: 54 km/hr Worked Example 2: Two trains of lengths 100m and 150m are running in opposite directions at speeds 40 km/hr and 50 km/hr respectively. In how much time will they cross each other?

1

Convert speeds to m/s: 40 km/hr = 40 × 5/18 = 100/9 m/s, 50 km/hr = 50 × 5/18 = 125/9 m/s

2

Relative speed = 100/9 + 125/9 = 225/9 = 25 m/s (opposite direction, so add)

3

Total distance = 100 + 150 = 250m

4

Time = Distance/Speed = 250/25 = 10 seconds Answer: 10 seconds Advanced Shortcut - Platform Formula: Time to cross platform = (Train length + Platform length)/Speed. This direct formula saves calculation steps in exams

→Most Common Trap

Students forget to add platform/bridge length when train crosses them. They only consider train length, leading to wrong answers. Always read whether the train crosses a pole (only train length) or platform/bridge (train length + platform/bridge length). Another frequent mistake is wrong unit conversion. Practice the 5/18 conversion thoroughly.

Many students confuse when to multiply or divide

⚡Speed-Distance-Time Shortcut

If train crosses pole in time T1 and platform in time T2, then platform length = speed × (T2 - T1). This eliminates the need to calculate train length first.

🔑 Key Points

Train crossing pole: Distance = Train length only
Train crossing platform/bridge: Distance = Train length + Platform/Bridge length
Speed conversion formula: km/hr to m/s multiply by 5/18, reverse multiply by 18/5
Relative speed for opposite directions: Add both speeds (S1 + S2)
Relative speed for same direction: Subtract speeds (S1 - S2)
Standard conversion: 72 km/hr = 20 m/s (memorize this)
Two trains crossing: Distance = Sum of both train lengths
Platform formula shortcut: Time = (Train length + Platform length)/Speed
Time difference method: Platform length = Speed × (T2 - T1)
Most common error: Forgetting to add platform length in crossing problems

📌 Exam Facts

Standard speed conversion factor from km/hr to m/s is 5/18
Standard speed conversion factor from m/s to km/hr is 18/5
When two trains move in opposite directions, relative speed equals sum of individual speeds
When two trains move in same direction, relative speed equals difference of individual speeds
Distance covered while crossing equals train length when crossing a pole or telegraph post
Distance covered while crossing platform equals train length plus platform length
72 km/hr equals exactly 20 m/s (frequently used in SSC problems)
Time taken by train to completely cross another train equals sum of lengths divided by relative speed

🚀 60-Second Revision

Remember: Pole crossing uses only train length, platform crossing adds platform length
Formula: Speed conversion km/hr to m/s multiply by 5/18
Trap: Always check if crossing pole or platform - different distance calculations
Shortcut: 72 km/hr = 20 m/s conversion for quick calculations
Relative speed: Add for opposite direction, subtract for same direction
Two trains: Total distance = Length1 + Length2, use relative speed
Platform trick: Time difference method gives platform length directly

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