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SSC CGL Relative Speed

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

SSC CGL 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

SSC CGL Relative Speed — Past Exam Questions

8 questions from actual SSC CGL papers · all shown free · click option to reveal solution

Exam Q 12019Previous 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 22020Previous 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 32018Previous 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 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 52019Previous 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 62020Previous 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

RELATIVE SPEED — COMPLETE GUIDE FOR SSC CGL ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

CORE CONCEPT — WHAT IS RELATIVE SPEED? ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Imagine you are sitting in a train moving at 60 km/h. Another train passes you at 80 km/h in the same direction. From your seat, the other train feels like it is moving at just 20 km/h — not 80 km/h. This 'felt' speed is called Relative Speed. In simple words: Relative Speed is the speed of one object as seen from another moving object.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ KEY RULES — THE TWO GOLDEN RULES

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Rule 1 — OPPOSITE DIRECTIONS:

When two objects move towards each other (or away from each other in opposite directions), their speeds ADD UP. Relative Speed = Speed A + Speed B

Rule 2 — SAME DIRECTION: When two objects move in the same direction, their speeds are SUBTRACTED.

Relative Speed = Speed A − Speed B (take the bigger minus the smaller) Memory Trick: OPPOSITE = ADD. SAME = SUBTRACT.

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Formula BlockMemorise — at least one formula appears in every paper

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1. Relative Speed (opposite directions) = u + v
2. Relative Speed (same direction) = u − v
3. Time to meet = Distance / Relative Speed
4. Distance covered = Relative Speed × Time
5. To convert km/h to m/s → multiply by 5/18
6. To convert m/s to km/h → multiply by 18/5

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Exam PatternsWhat examiners ask — read before attempting PYQs

— HOW IT IS ASKED ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ SSC CGL asks Relative Speed in 4 main ways: → Two trains crossing each other (most common) → A person running towards or away from a train → Two people walking towards or away from each other → Boats and streams (a special form of relative speed) In train problems, always remember: the TOTAL DISTANCE = Length of Train 1 + Length of Train 2 (when crossing each other). If a train crosses a stationary pole or person, distance = only the train's own length. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

ShortcutsUse these to save 30–60 seconds per question

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Trick 1 — TIME TO MEET SHORTCUT: If two people start from opposite ends of a road of length D km, walking at speeds u and v: Time to meet = D / (u + v) Trick 2 — TRAIN CROSSING A MOVING PERSON: If a train of length L moves at speed T and a person walks at speed P in the SAME direction: Time to cross = L / (T − P) If they move in OPPOSITE directions: Time to cross = L / (T + P) Trick 3 — FIND ORIGINAL SPEED WHEN MEETING TIME IS GIVEN: If two trains A and B start at the same time from stations X and Y towards each other and meet after time T: Speed of A / Speed of B = Distance covered by A / Distance covered by B This ratio stays constant and is extremely useful in advanced problems. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Worked ExampleSolve this step-by-step before moving on

— TRAINS CROSSING (OPPOSITE DIRECTION) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Question: Two trains of lengths 120 m and 80 m are moving towards each other at 60 km/h and 40 km/h. How long will they take to cross each other? Step 1 — Total distance to cover = 120 + 80 = 200 m Step 2 — Relative Speed = 60 + 40 = 100 km/h (opposite directions, so ADD) Step 3 — Convert to m/s: 100 × 5/18 = 500/18 = 27.78 m/s Step 4 — Time = Distance / Speed = 200 / (500/18) = 200 × 18/500 = 3600/500 = 7.2 seconds Answer: 7.2 seconds ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ WORKED EXAMPLE 2 — SAME DIRECTION, PERSON WALKING ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Question: A train 150 m long runs at 54 km/h. A man runs at 18 km/h in the same direction.

In how many seconds will the train pass the man? Step 1 — Relative Speed = 54 − 18 = 36 km/h (same direction, SUBTRACT) Step 2 — Convert to m/s: 36 × 5/18 = 10 m/s Step 3 — Distance = length of train = 150 m (man is a point object) Step 4 — Time = 150 / 10 = 15 seconds Answer: 15 seconds ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ #1 MOST COMMON TRAP — DO NOT FALL FOR THIS ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ TRAP: Students forget to ADD the lengths of BOTH trains when two trains cross each other. They use only one train's length. This gives a completely wrong answer.

Always check — are both objects moving? If yes, total distance = sum of both lengths. If one object is a pole or a standing person, distance = only the moving train's length.

Key Points to Remember

  • Relative Speed = Speed A + Speed B when objects move in OPPOSITE directions
  • Relative Speed = Speed A − Speed B when objects move in the SAME direction
  • When two trains cross each other, total distance = Length of Train 1 + Length of Train 2
  • When a train crosses a pole or standing person, distance = only the train's own length
  • Formula: Time to meet = Total Distance / Relative Speed
  • Conversion shortcut: km/h to m/s → multiply by 5/18; m/s to km/h → multiply by 18/5
  • If two people walk towards each other from distance D at speeds u and v, they meet in D/(u+v) hours
  • Boats and streams is a special case of relative speed — downstream adds, upstream subtracts
  • Trick: Same direction problems almost always require subtraction — the slower object seems almost still to the faster one
  • If a train of length L crosses a moving man at speed P in opposite direction: Time = L / (Train Speed + P)

Exam-Specific Tips

  • To convert km/h into m/s, multiply by 5/18 — this constant appears in almost every train/speed question
  • Two objects moving toward each other cover their combined distance at a rate equal to the sum of their speeds
  • The time for two trains to completely cross each other = (L1 + L2) / Relative Speed, where L1 and L2 are their lengths
  • If both trains move in the same direction, relative speed = difference of their speeds; if in opposite directions, relative speed = sum of their speeds
  • A train crossing a stationary pole uses only its own length as the distance, not the pole's width
  • If two trains start simultaneously from two points and travel toward each other, the ratio of their speeds equals the ratio of distances covered at the time of meeting
  • For a man running in the same direction as a train: effective speed of train over man = Train Speed − Man Speed
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 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 3easy

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 4easy

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 5easy

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 6easy

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 7easy

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 8easy

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 9easy

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 10easy

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 11easy

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 12easy

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 13easy

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 14easy

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 15easy

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 16easy

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 17easy

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 18easy

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 19easy

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 20medium

Two cyclists start from the same point and travel in the same direction. Cyclist A travels at 15 km/h and Cyclist B travels at 10 km/h. After how many hours will Cyclist A be 20 km ahead of Cyclist B?

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60-Second Revision — Relative Speed

  • Remember: OPPOSITE directions → ADD speeds; SAME direction → SUBTRACT speeds
  • Formula: Time = Distance / Relative Speed — always convert units to match (km/h or m/s)
  • Trap: Two trains crossing? Distance = BOTH lengths added. Train crossing a pole? Distance = ONE train length only
  • Convert km/h to m/s → multiply by 5/18. Convert m/s to km/h → multiply by 18/5
  • Formula for time to meet head-on: T = D / (u + v) where D is initial gap between the two objects
  • Train crossing a moving man → use relative speed, distance = train length only
  • Quick check before solving: Are both objects moving? What direction? This decides ADD or SUBTRACT
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