Study Material — 16 PYQs (2022–2022) · Concept Notes · Shortcuts
SBI PO Relative Speed is a frequently tested subtopic — 16 previous year questions from 2022–2022 papers are included below with concept notes, key rules and shortcut tricks.
16 questions from actual SBI PO papers · all shown free · click option to reveal solution
Exam Q 12022Previous Year Pattern
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 150 km apart, in how many hours will they meet?
Exam Q 22022Previous 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 32022Previous Year Pattern
Two buses start from the same point and travel in opposite directions. Bus X travels at 50 km/h and Bus Y travels at 70 km/h. After how many hours will they be 360 km apart?
Exam Q 42022Previous Year Pattern
A boat travels upstream at 8 km/h and downstream at 12 km/h. What is the speed of the boat in still water?
Exam Q 52022Previous Year Pattern
A runner and a cyclist start from the same point and travel in the same direction. The runner's speed is 12 km/h and the cyclist's speed is 20 km/h. How far ahead will the cyclist be after 2.5 hours?
Exam Q 62022Previous Year Pattern
Two cars travel towards each other from two cities that are 240 km apart. Car A travels at 45 km/h and Car B travels at 75 km/h. At what distance from Car A's starting point will they meet?
Exam Q 72022Previous Year Pattern
Two trains A and B 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?
Exam Q 82022Previous 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 of the man, how long will it take for the man to catch up with the woman?
Exam Q 92022Previous Year Pattern
A boat travels 48 km downstream in 3 hours and 48 km upstream in 6 hours. What is the speed of the boat in still water?
Exam Q 102022Previous Year Pattern
Two runners start from the same point and run in the same direction. Runner X runs at 12 m/s and Runner Y runs at 8 m/s. After how many seconds will Runner X be exactly 200 metres ahead of Runner Y?
Exam Q 112022Previous Year Pattern
A car and a motorcycle start from opposite ends of a 360 km highway and travel towards each other. The car travels at 80 km/h and the motorcycle at 100 km/h. At what distance from the car's starting point will they meet?
Exam Q 122022Previous Year Pattern
Two cyclists start simultaneously from points A and B, which are 90 km apart. They cycle towards each other at speeds of 18 km/h and 27 km/h respectively. After how many minutes will they meet?
Exam Q 132022Previous Year Pattern
Two trains, A and B, start simultaneously from stations X and Y respectively, which are 480 km apart. Train A travels towards Y at 60 km/h, while train B travels towards X at 40 km/h. After how much time will they meet, and at what distance from station X?
Exam Q 142022Previous Year Pattern
A boat travels 120 km downstream in 4 hours and 120 km upstream in 6 hours. A swimmer can swim at the same speed as the boat's speed in still water. How long will the swimmer take to cover 90 km in still water?
Exam Q 152022Previous Year Pattern
Two cyclists start from the same point and travel in the same direction on a circular track of 400 m. Cyclist A travels at 8 m/s and Cyclist B at 6 m/s. After how much time will Cyclist A lap Cyclist B for the first time (i.e., be exactly 400 m ahead)?
Exam Q 162022Previous Year Pattern
Two runners, P and Q, run on a 500 m circular track. P runs at 10 m/s and Q at 8 m/s, both starting from the same point in the same direction. How many times will P lap Q before P completes 10 full laps?
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
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