This page covers Agniveer Army CEE Relative Speed with complete concept notes, 8 graded practice MCQs, key points and exam-specific tips. Free to study.
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
8graded MCQs · easy to hard · full solution & trap analysis
A car travelling at 80 km/h is 15 km behind another car travelling at 50 km/h in the same direction. How long will it take for the faster car to catch up?
Practice 2easy
Two cyclists start from the same point and travel in opposite directions. One cycles at 12 km/h and the other at 18 km/h. After how many hours will they be 90 km apart?
Practice 3easy
Two trains start from opposite ends of a 300 km track and move towards each other. Train A travels at 60 km/h and Train B travels at 40 km/h. How long will it take for them to meet?
Practice 4medium
A boat moves downstream at 25 km/h and upstream at 15 km/h. If the boat's speed in still water is b km/h and the stream's speed is s km/h, find the stream's speed.
Practice 5medium
Two runners start from the same point and run in opposite directions on a circular track. Runner X runs at 12 m/s and Runner Y runs at 8 m/s. After how many seconds will they meet again if the track length is 400 m?
Practice 6medium
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. What is their relative speed?
Practice 7medium
A car travels at 80 km/h and a motorcycle travels at 50 km/h in the same direction on the same road. What is their relative speed?
Practice 8hard
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, and Train Y travels from B towards A at 40 km/h. After how many hours will the two trains meet?
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