Core ConceptRead this first — the foundation of the topic
Speed, Distance, and Time form the foundation of motion problems in SSC CGL. This topic appears in 2-3 questions per exam and requires strong formula application skills. Core Concept: Speed measures how fast an object moves. Distance is the path covered. Time is the duration taken. These three are linked by a simple relationship that forms the base of all calculations.
Formula BlockMemorise — at least one formula appears in every paper
• Speed = Distance/Time (S = D/T)
• Distance = Speed × Time (D = S × T)
• Time = Distance/Speed (T = D/S)
Unit Conversions (Critical for SSC):
• km/hr to m/s: Multiply by 5/18
• m/s to km/hr: Multiply by 18/5
• 1 km/hr = 5/18 m/s
Exam PatternsWhat examiners ask — read before attempting PYQs
Shortcut 1 - Unit Conversion Trick
To convert km/hr to m/s, multiply by 5/18
Remember
36 km/hr = 10 m/s (this is a standard conversion to memorize)
Shortcut 2 - Distance Formula Rearrangement
When speed increases by x%, new time = Original time × 100/(100+x)
When speed decreases by x%, new time = Original time × 100/(100-x)
Worked ExampleSolve this step-by-step before moving on
Convert to m/s
Speed in m/s = 60 × 5/18 = 300/18 = 16.67 m/s
Answer: 16.67 m/s
Worked Example 2:
A train running at 54 km/hr takes 20 seconds to cross a platform 200m long. Find the length of the train.
1
Step 1
Convert speed to m/s
54 km/hr = 54 × 5/18 = 15 m/s
2
Step 2
Find total distance covered
Distance = Speed × Time = 15 × 20 = 300m
3
Step 3
Find train length
Train length = Total distance - Platform length = 300 - 200 = 100m
Answer: 100 meters
Shortcut 3 - Relative Speed:
• Same direction: Relative speed = |S1 - S2|
• Opposite direction: Relative speed = S1 + S2
Most Common Trap (#1 Mistake):
Students forget unit conversions! SSC deliberately mixes km/hr and m/s in the same question. Always check units in options and convert accordingly. Questions asking for train crossing times usually need m/s, while car journey problems often use km/hr.
Another frequent error is confusing relative motion directions. When two objects move toward each other, add their speeds. When moving in the same direction, subtract speeds.
Time-based problems often trick students with percentage changes in speed. Remember: if speed increases by 25%, time decreases by 20% (not 25%). Use the reciprocal relationship carefully.
Practice identifying whether the question asks for train length, crossing time, or platform length. Each requires different approaches but uses the same core formula.
Two cars start from the same point and travel in the same direction. Car A travels at 60 km/h and Car B travels at 80 km/h. After how many hours will Car B be 100 km ahead of Car A?
Practice 2easy
A boat travels 48 km downstream in 3 hours and 48 km upstream in 4 hours. What is the speed of the boat in still water?
Practice 3easy
A cyclist covers 150 km in 5 hours. If he increases his speed by 10 km/h, how long will he take to cover the same distance?
Practice 4easy
A man walks at 5 km/h and covers a distance in 6 hours. If he walks at 6 km/h, how much time will he save?
Practice 5easy
A train travels at 90 km/h. How far will it travel in 2 hours and 30 minutes?
Practice 6medium
Rajesh cycles at 15 km/h and covers a certain distance in 8 hours. If he cycles at 20 km/h, in how many hours will he cover the same distance?
Practice 7medium
Two runners, A and B, start from the same point. A runs at 12 km/h and B runs at 8 km/h in the same direction. After how many hours will A be 20 km ahead of B?
Practice 8medium
A car travels from City A to City B at 60 km/h and returns at 40 km/h. If the distance between the cities is 120 km, what is the average speed for the entire journey (in km/h)?
Practice 9medium
A boat travels 84 km downstream in 6 hours and 84 km upstream in 12 hours. What is the speed of the boat in still water (in km/h)?
Practice 10medium
A man walks 3 km in 45 minutes. If he walks at the same pace, how far will he walk in 2 hours 15 minutes?
Practice 11medium
A train travels 240 km in 4 hours at constant speed. If it needs to cover 360 km at the same speed, how much additional time (in hours) will it require beyond the initial 4 hours?
Practice 12hard
Two cyclists, Raj and Priya, start from the same point and travel in the same direction on a circular track of length 400 metres. Raj cycles at 8 m/s and Priya at 6 m/s. After how many seconds will Raj lap Priya for the first time (i.e., be exactly one full lap ahead)?
Practice 13hard
A boat travels upstream for 120 km in 8 hours and downstream for the same distance in 5 hours. If the boat's speed in still water is B km/h and the current's speed is C km/h, what is the value of B² - C²?
Practice 14hard
A person walks from Point P to Point Q at 4 km/h, and returns from Q to P at 6 km/h. The total time taken for the round trip is 5 hours. What is the distance between P and Q?
Practice 15hard
A car travels from City X to City Y. If it travels at 50 km/h, it reaches 2 hours late. If it travels at 70 km/h, it reaches 1 hour early. What is the distance between City X and City Y?
60-Second Revision — Speed Distance Time
Formula: Speed = Distance/Time, Distance = Speed × Time, Time = Distance/Speed
Remember: 36 km/hr = 10 m/s for quick conversions
Unit conversion: km/hr to m/s multiply by 5/18
Trap: Always check if answer needs km/hr or m/s units
Relative speed: Add for opposite directions, subtract for same direction