Study Material — 11 PYQs (2021–2021) · Concept Notes · Shortcuts
SSC CPO Relative Speed is a frequently tested subtopic — 11 previous year questions from 2021–2021 papers are included below with concept notes, key rules and shortcut tricks.
11 questions from actual SSC CPO papers · all shown free · click option to reveal solution
Exam Q 12021Previous Year Pattern
Two cars start from the same location and travel towards each other on a straight road. Car P travels at 55 km/h and Car Q travels at 65 km/h. If they meet after 4 hours, what was the initial distance between them?
Exam Q 22021Previous Year Pattern
A runner jogs at 12 km/h and a cyclist rides at 18 km/h, both starting from the same point in the same direction. After 2 hours, how far ahead is the cyclist from the runner?
Exam Q 32021Previous Year Pattern
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?
Exam Q 42021Previous Year Pattern
Two trains of lengths 150 m and 100 m are running towards each other on parallel tracks at speeds of 50 km/h and 40 km/h respectively. How many seconds will they take to completely pass each other?
Exam Q 52021Previous Year Pattern
A train 240 metres long is travelling at 45 km/h. How long will it take to pass a stationary pole?
Exam Q 62021Previous Year Pattern
Two cyclists start from the same point and travel in opposite directions. Cyclist A travels at 18 km/h and Cyclist B travels at 12 km/h. After how many hours will they be 90 km apart?
Exam Q 72021Previous Year Pattern
Two trains are running 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?
Exam Q 82021Previous Year Pattern
Two trains start simultaneously from stations A and B, which are 480 km apart. Train X travels from A to B at 60 km/h, while Train Y travels from B to A at 40 km/h. A bird flies back and forth between the two trains at a constant speed of 80 km/h, starting from Train X. What is the total distance covered by the bird from the moment the trains start until they meet?
Exam Q 92021Previous Year Pattern
A train 150 m long travels at 72 km/h. A man stands on a platform. How long does the train take to completely pass the man?
Exam Q 102021Previous Year Pattern
A boat travels 120 km downstream in 4 hours and 120 km upstream in 6 hours. A second boat travels at twice the speed of the current. How long will the second boat take to travel 180 km downstream?
Exam Q 112021Previous Year Pattern
Two cars start from the same point on a circular track of circumference 600 m. Car A travels at 15 m/s and Car B travels at 10 m/s, both in the same direction. After how much time will Car A lap Car B for the second time?
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
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?
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
4graded MCQs · easy to hard · full solution & trap analysis
Two buses start from the same point and travel in opposite directions. Bus X travels at 50 km/h and Bus Y travels at 30 km/h. After how many hours will they be 240 km apart?
Practice 2easy
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 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 man starts 50 km behind the woman, how long will it take for the man to catch up with the woman?
Practice 4easy
A boat travels upstream at 8 km/h and downstream at 12 km/h. What is the speed of the boat in still water?
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