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
16graded MCQs · easy to hard · full solution & trap analysis
Two cyclists start from opposite ends of a 90 km road. Cyclist X travels at 18 km/h and Cyclist Y travels at 12 km/h towards each other. At what distance from Cyclist X's starting point will they meet?
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 woman starts 20 km ahead, how long will it take the man to catch up with the woman?
Practice 4easy
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 5easy
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 much time will they be 60 km apart?
Practice 6easy
A car travels 240 km in 4 hours. A bus travels at a speed 10 km/h less than the car. How long will the bus take to cover the same 240 km distance?
Practice 7medium
A car and a motorcycle start from the same point and travel in the same direction. The car travels at 80 km/h and the motorcycle at 60 km/h. After 2 hours, the motorcycle increases its speed to 90 km/h. How much time will it take for the motorcycle to catch up with the car from that point onwards?
Practice 8medium
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 9medium
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 30 km behind the woman, how long will it take the man to catch up with the woman?
Practice 10medium
A person walks at 4 km/h and reaches a destination 2 hours late. If he walks at 5 km/h, he reaches 1 hour early. What is the distance to the destination?
Practice 11hard
Two trains A and B are running towards each other on parallel tracks. Train A travels at 72 km/h and Train B travels at 54 km/h. If they are initially 315 km apart, after how many hours will they meet?
Practice 12hard
A man cycles at 16 km/h and a woman cycles at 12 km/h in the same direction on the same road. If the woman starts 48 km ahead of the man, how long will it take the man to catch up with the woman?
Practice 13hard
Two boats start from the same point and travel in opposite directions on a river. Boat X travels at 20 km/h and Boat Y travels at 15 km/h. After 3 hours, they turn around and travel towards each other at the same speeds. How much time (in hours) will it take them to meet after they turn around?
Practice 14hard
A car travels from City P to City Q at 60 km/h. On the return journey from Q to P, it travels at 40 km/h. If the total time taken for the round trip is 10 hours, what is the distance between the two cities?
Practice 15hard
A swimmer can swim at 8 km/h in still water. The speed of the current is 2 km/h. If the swimmer swims upstream for 2 hours and then downstream for 1.5 hours, what is the total distance covered?
Practice 16hard
Two runners start from the same point on a circular track of length 400 metres. Runner A runs at 8 m/s and Runner B runs at 6 m/s in the same direction. After how many seconds will Runner A lap Runner B for the first time (i.e., be exactly 400 metres ahead)?
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