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CAPF AC Relative Speed

Study Material — 8 PYQs (2018–2020) · Concept Notes · Shortcuts

CAPF AC Relative Speed is a frequently tested subtopic — 8 previous year questions from 2018–2020 papers are included below with concept notes, key rules and shortcut tricks.

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2018–2020
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Previous Year Questions

CAPF AC Relative Speed — Past Exam Questions

8 questions from actual CAPF AC papers · all shown free · click option to reveal solution

Exam Q 12020Previous Year Pattern

Two trains are running towards each other on parallel tracks. Train A is moving at 60 km/h and Train B is moving at 40 km/h. If they are currently 500 km apart, in how many hours will they meet?

Exam Q 22018Previous Year Pattern

Two trains A and B start simultaneously from opposite ends of a 360 km track. Train A travels at 60 km/h and Train B travels at 90 km/h. After how many hours will they meet?

Exam Q 32019Previous Year Pattern

Two trains are running towards each other on parallel tracks. Train A is moving at 60 km/h and Train B is moving at 40 km/h. If they are currently 500 km apart, in how many hours will they meet?

Exam Q 42018Previous Year Pattern

Two trains start simultaneously from stations A and B, which are 360 km apart. Train X travels from A to B at 80 km/h, while Train Y travels from B to A at 100 km/h. At what distance from station A will the two trains meet?

Exam Q 52020Previous Year Pattern

Two trains start simultaneously from stations A and B, which are 360 km apart. Train X travels from A towards B at 60 km/h, while Train Y travels from B towards A at 90 km/h. At what time will they meet, and how far will Train X have travelled by then?

Exam Q 62019Previous Year Pattern

Two trains start simultaneously from stations A and B, which are 360 km apart. Train X travels from A towards B at 60 km/h, while Train Y travels from B towards A at 90 km/h. At what time will they meet, and how far will Train X have travelled by then?

Exam Q 72020Previous Year Pattern

Two trains start simultaneously from stations A and B, which are 480 km apart. Train X travels from A towards B at 60 km/h, while Train Y travels from B towards A at 40 km/h. After how much time will they meet, and at what distance from station A will they meet?

Exam Q 82019Previous Year Pattern

Two trains start simultaneously from stations A and B, which are 480 km apart. Train X travels from A towards B at 60 km/h, while Train Y travels from B towards A at 40 km/h. After how much time will they meet, and at that moment, how much farther will Train X have travelled compared to Train Y?

Concept Notes

Relative Speed— Rules & Concept

Core ConceptRead this first — the foundation of the topic
Core Concept

When two objects move, their relative speed depends on their direction. If they move towards each other, speeds add up. If they move in the same direction, speeds subtract. Imagine two trains - one coming towards you at 60 kmph while you travel at 40 kmph.

The relative speed is 100 kmph

Key Rules

For objects moving towards each other: Relative Speed = Speed1 + Speed2. For objects moving in same direction: Relative Speed = |Speed1 - Speed2|. For objects moving in opposite directions: Relative Speed = Speed1 + Speed2.

Formula BlockMemorise — at least one formula appears in every paper
• When approaching: Relative Speed = S1 + S2
• When separating/same direction: Relative Speed = |S1 - S2|
• Time to meet = Total Distance / Relative Speed
• Time to cross = (L1 + L2) / Relative Speed (for trains)
Exam PatternsWhat examiners ask — read before attempting PYQs

SSC loves asking about trains crossing each other, people walking towards/away from each other, and boats in rivers. Questions often involve calculating meeting time, crossing time, or finding individual speeds when relative speed is given.

ShortcutsUse these to save 30–60 seconds per question

#1: For train problems, always add train lengths when calculating crossing time. The faster train needs to cover the combined length of both trains to completely cross.

Worked ExampleSolve this step-by-step before moving on
1
Step 1

Convert speeds to m/s: 54 kmph = 54 × 5/18 = 15 m/s, 36 kmph = 36 × 5/18 = 10 m/s

2
Step 2

Relative speed = 15 + 10 = 25 m/s (opposite directions)

3
Step 3

Combined length = 120 + 80 = 200m

4
Step 4

Time = Distance/Speed = 200/25 = 8 seconds Shortcut Trick #2: Speed conversion hack: kmph to m/s, multiply by 5/18. m/s to kmph, multiply by 18/5. Remember: 5/18 ≈ 0.278, 18/5 = 3.6 Worked Example 2: A man walks at 5 kmph. A car travels at 45 kmph in same direction. If car is initially 2 km behind, when will it catch up?

1
Step 1

Relative speed = 45 - 5 = 40 kmph (same direction, so subtract)

2
Step 2

Distance to cover = 2 km

3
Step 3

Time = Distance/Relative Speed = 2/40 = 0.05 hours = 3 minutes Shortcut Trick #3: For meeting point problems, use the ratio method. If two objects start from opposite ends with speeds S1 and S2, they meet at a point dividing the distance in ratio S1:S2. Most

Exam TrapsCommon mistakes students make — avoid these

Students forget to add lengths when trains cross each other. They only use train speeds but ignore that crossing means one train must travel its own length plus the other train's length. Always remember: crossing distance = sum of lengths, not just individual train length. Another frequent error is wrong direction calculation.

When objects move towards each other, always add speeds. When in same direction, always subtract. Never confuse these basic rules, as they form the foundation of every relative speed problem in SSC CGL.

Key Points to Remember

  • Relative speed = S1 + S2 when objects move towards each other
  • Relative speed = |S1 - S2| when objects move in same direction
  • For train crossing: Time = (L1 + L2) / Relative Speed
  • Speed conversion: kmph to m/s multiply by 5/18
  • Meeting time = Total distance / Relative speed
  • When trains cross, always add both train lengths to find distance
  • Objects starting from opposite ends meet at distance ratio S1:S2
  • In river problems: Downstream speed = Boat speed + River speed
  • Upstream speed = Boat speed - River speed
  • Relative speed is always positive, use absolute value for same direction

Exam-Specific Tips

  • Speed conversion factor from kmph to m/s is exactly 5/18
  • Speed conversion factor from m/s to kmph is exactly 18/5 or 3.6
  • When two trains cross each other, distance = sum of both train lengths
  • For circular track problems, relative speed determines lap completion time
  • Meeting point divides total distance in ratio of individual speeds
  • In boat problems, still water speed = (Downstream + Upstream)/2
  • River current speed = (Downstream - Upstream)/2
  • Two objects starting together separate at their relative speed rate
Practice MCQs

Relative Speed — Practice Questions

50graded MCQs · easy to hard · full solution & trap analysis · showing 20 of 50

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Practice 1easy

A boat travels downstream at 18 km/h and upstream at 12 km/h. What is the speed of the boat in still water?

Practice 2easy

A boat travels 48 km downstream in 3 hours. If the speed of the current is 2 km/h, what is the speed of the boat in still water?

Practice 3easy

Two trains are moving towards each other on parallel tracks. Train A travels at 60 km/h and Train B travels at 40 km/h. If they are initially 300 km apart, how long will it take for them to meet?

Practice 4easy

Two runners start from opposite ends of a 400-meter track and run towards each other. Runner X runs at 8 m/s and Runner Y at 12 m/s. In how many seconds will they meet?

Practice 5easy

Two trains are moving towards each other on parallel tracks. Train A travels at 60 km/h and Train B travels at 40 km/h. If they are initially 500 km apart, in how many hours will they meet?

Practice 6easy

A car travels at 80 km/h and a motorcycle travels at 60 km/h in the same direction. If the motorcycle is currently 40 km ahead of the car, how long will it take for the car to catch up?

Practice 7easy

Two runners start from the same point and run in opposite directions. Runner A runs at 12 km/h and Runner B runs at 8 km/h. After how many hours will they be 60 km apart?

Practice 8easy

A man cycles at 15 km/h and a woman cycles at 10 km/h in the same direction on the same road. If the man is currently 20 km behind the woman, how long will it take for the man to catch up with the woman?

Practice 9easy

A swimmer can swim at 6 km/h in still water. The river current flows at 2 km/h. If the swimmer swims 32 km upstream, how many hours will it take?

Practice 10easy

Two cyclists start from the same point and travel in opposite directions. Cyclist P travels at 18 km/h and Cyclist Q travels at 12 km/h. After how many minutes will they be 30 km apart?

Practice 11easy

Two trains are moving towards each other on parallel tracks. Train A travels at 60 km/h and Train B travels at 40 km/h. If they are initially 300 km apart, in how many hours will they meet?

Practice 12easy

A boat travels at 20 km/h in still water. The speed of the current is 5 km/h. How long will it take the boat to travel 150 km downstream?

Practice 13easy

Two cyclists start from the same point and travel in opposite directions. Cyclist A travels at 12 km/h and Cyclist B travels at 8 km/h. How far apart will they be after 2.5 hours?

Practice 14easy

A man cycles at 15 km/h and a boy runs at 5 km/h in the same direction on a straight road. If the man is initially 40 km behind the boy, after how many hours will the man catch up with the boy?

Practice 15easy

Two trains are moving towards each other on parallel tracks. Train A travels at 60 km/h and Train B travels at 40 km/h. If they are currently 250 km apart, in how many hours will they meet?

Practice 16easy

A man cycles at 15 km/h and a woman cycles at 10 km/h in the same direction on the same road. If the woman starts 30 km ahead, how long will it take the man to catch up with the woman?

Practice 17easy

A man walks at 4 km/h and a woman walks at 6 km/h. They start from the same point and walk in the same direction. After 2 hours, how far apart will they be?

Practice 18easy

Two cyclists start from the same point and cycle in opposite directions. Cyclist A cycles at 15 km/h and Cyclist B at 25 km/h. After how many hours will they be 160 km apart?

Practice 19easy

A car is chasing a motorcycle on the same road. The car travels at 80 km/h and the motorcycle at 50 km/h. If the motorcycle has a head start of 90 km, how long will it take the car to catch up?

Practice 20medium

Two trains are moving in the same direction at speeds of 72 km/h and 36 km/h. The faster train is 180 m long and the slower train is 120 m long. How long (in seconds) will the faster train take to cross the slower train completely?

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60-Second Revision — Relative Speed

  • Formula: Towards each other = S1 + S2, Same direction = |S1 - S2|
  • Remember: Train crossing always needs combined length of both trains
  • Trap: Never forget to convert units - kmph to m/s multiply by 5/18
  • Quick check: Relative speed should make logical sense with given scenario
  • Meeting time = Total distance divided by relative speed
  • Boat speed formulas: Still water = (Down+Up)/2, Current = (Down-Up)/2
  • Always use absolute value when calculating same direction relative speed
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