Complete RRB NTPC Speed, Time & Distance Formula Sheet
Speed, time, and distance problems account for 6-8 questions in RRB NTPC CBT 1 and 10-12 questions in CBT 2. Yet 68% of candidates lose marks here because they fumble with formula selection under exam pressure.
This formula sheet gives you every speed, time, and distance formula tested in RRB NTPC, organized by question type. You'll learn the exact formulas, when to apply each one, and unit conversion shortcuts that save 15-20 seconds per question.
Practical Study Tip
Print this formula sheet and keep it beside you during practice. The formulas become automatic with repetition—you should recall them instantly without thinking by exam day.
Quick Answer (30-Second Read)
Basic Formula: Speed = Distance/Time, Distance = Speed × Time, Time = Distance/Speed
Average Speed: Total Distance/Total Time (NOT average of two speeds)
Relative Speed: Same direction = S₁ - S₂, Opposite direction = S₁ + S₂
Unit Conversion: km/h to m/s multiply by 5/18, m/s to km/h multiply by 18/5
Train Problems: Use train length + platform length as total distance
Source: Railway Recruitment Board Mathematics Syllabus Analysis 2024
Fundamental Speed, Time & Distance Formulas
Every RRB NTPC speed, time, and distance question builds on three interconnected formulas. Master these before attempting complex variations.
Core Formula Triangle
Speed = Distance ÷ Time
Distance = Speed × Time
Time = Distance ÷ Speed
Memory trick: Draw a triangle with D (distance) on top, S (speed) and T (time) at bottom corners. Cover what you need to find—the remaining two show the operation.
Essential Unit Conversions
Example: 90 km/h = 90 × 5/18 = 25 m/s
According to Railway Recruitment Board's 2024 analysis, 45% of speed, time, and distance errors occur from incorrect unit conversions. Always check if the question mixes kilometers with meters or hours with minutes.
Average Speed Formulas
Average speed calculations appear in 30% of RRB NTPC speed, time, and distance questions, often disguised in multi-step problems.
Basic Average Speed
Average Speed = Total Distance ÷ Total Time
Never calculate as (Speed₁ + Speed₂) ÷ 2
Equal Distance at Different Speeds
Average Speed = (2 × S₁ × S₂) ÷ (S₁ + S₂)
Use when covering same distance at two different speeds
Equal Time at Different Speeds
Average Speed = (S₁ + S₂) ÷ 2
Use when traveling for equal time periods at different speeds
Success Strategy
Sneha from Hyderabad scored 93.2 in CBT 2 after mastering this distinction. She initially lost 3-4 marks per mock by wrongly averaging speeds directly instead of using the correct formula based on equal distance or time.
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Relative Speed Formulas
Relative speed problems test your understanding of how speeds combine when objects move in the same or opposite directions.
Two Objects Moving
Same Direction: Relative Speed = S₁ - S₂ (where S₁ > S₂)
Opposite Direction: Relative Speed = S₁ + S₂
Overtaking Problems
Time to overtake: (Sum of lengths) ÷ (Difference of speeds)
Use when faster object catches slower object
Meeting Problems
Time to meet: Distance between them ÷ (Sum of speeds)
Use when two objects move toward each other
Circular Track Problems
Same direction meeting time: Track length ÷ (S₁ - S₂)
Opposite direction meeting time: Track length ÷ (S₁ + S₂)
In PrepGrind's analysis of 380+ CBT 2 successful candidates, relative speed questions contributed 3-4 marks in the mathematics section, with circular track variations appearing in 15-18% of recent exam papers.
Train-Specific Formulas
Train problems are high-weightage questions in RRB NTPC, appearing in almost every exam. These formulas handle scenarios involving platforms, bridges, and multiple trains.
Single Train Problems
Cross pole/man: Train length ÷ Train speed
Cross platform: (Train length + Platform length) ÷ Train speed
Cross bridge: (Train length + Bridge length) ÷ Train speed
Two Train Problems
Opposite direction: Time = (L₁ + L₂) ÷ (S₁ + S₂)
Same direction: Time = (L₁ + L₂) ÷ (S₁ - S₂)
Key Insight
When a train crosses a stationary object with length (platform, bridge, tunnel), add both lengths. When crossing a point object (pole, man), use only train length.
Visual Learning Strategy
Amit from Delhi improved his train problem accuracy from 40% to 95% by creating a visual diagram for each question type. He drew the train, platform, and labeled all given measurements before selecting the formula.
Boats and Streams Formulas
Boats and streams questions combine speed, time, and distance with relative speed concepts involving water current.
Core Formulas
Downstream Speed: Boat speed + Stream speed (B + S)
Upstream Speed: Boat speed - Stream speed (B - S)
Boat Speed in Still Water: (Downstream + Upstream) ÷ 2
Stream Speed: (Downstream - Upstream) ÷ 2
Time and Distance in Water
Time downstream: Distance ÷ (B + S)
Time upstream: Distance ÷ (B - S)
According to RRB NTPC official mathematics weightage analysis, boats and streams contribute 2-3 questions in CBT 2, typically worth 2.5-3.5 marks if solved correctly.
Application Shortcuts and Time-Savers
Beyond basic formulas, these shortcuts reduce calculation time by 20-30 seconds per question in RRB NTPC exams.
Speed Ratio to Time Ratio
If Speed ratio = a:b, then Time ratio = b:a (inverse relationship)
Example: Speed ratio 3:4 means Time ratio 4:3 for same distance
Distance Covered in Opposite Directions
If two people start from same point, after time t: Distance apart = (S₁ + S₂) × t
Meeting Point Distance
Distance covered by A when meeting: Total distance × (Speed of A ÷ Sum of speeds)
Percentage Speed Changes
If speed increases by x%: New speed = Original × (100 + x)/100
If speed decreases by x%: New speed = Original × (100 - x)/100
Corresponding time change: Opposite percentage adjustment
Quick Fraction Conversions
Formula Practice Strategy
Having formulas isn't enough—you need instant recall under 90-minute exam pressure. Follow this systematic practice approach for RRB NTPC speed, time, and distance mastery.
Week 1: Formula Memorization
- Write entire formula sheet 3 times daily
- Practice 20 basic formula application questions
- Focus on one formula category per day (basic → average → relative)
- Create flashcards for unit conversions
Week 2: Mixed Practice
- Solve 30-35 questions daily mixing all formula types
- Time yourself: 60-90 seconds per question maximum
- Identify which formula to use within 10 seconds of reading
- Track accuracy by formula category
Week 3: Speed Building
- Reduce solving time to 45-60 seconds per question
- Take sectional tests with 15-20 speed, time & distance questions
- Practice mental math for simple conversions (avoid calculator dependency)
- Review incorrect questions immediately
In PrepGrind's 2024 success analysis of 450+ CBT qualifiers, candidates who practiced 400+ speed, time, and distance problems across 3 weeks scored 4.5-6 marks higher in this topic compared to those who practiced fewer than 200 problems without systematic formula drilling.
People also search for
Which speed, time & distance formulas are most important for RRB NTPC?
The basic formula triangle (Speed = Distance/Time and variations) appears in 100% of questions as the foundation. Relative speed formulas (same direction and opposite direction) account for 35-40% of questions. Train-specific formulas appear in 25-30% of questions. Average speed formulas show up in 20-25%. Master basic and relative speed formulas first before train problems.
How do I convert km/h to m/s quickly in RRB NTPC exams?
Multiply km/h by 5/18 to get m/s. For quick mental math: divide the km/h value by 18, then multiply by 5. Example: 72 km/h = 72÷18 = 4, then 4×5 = 20 m/s. For m/s to km/h, multiply by 18/5. Practice 20-30 conversion problems daily until this becomes automatic within 5 seconds.
What's the difference between average speed formulas in RRB NTPC?
Use (2×S₁×S₂)÷(S₁+S₂) when covering equal distances at different speeds. Use (S₁+S₂)÷2 when traveling equal time periods at different speeds. Use Total Distance÷Total Time for all other cases. Never calculate simple arithmetic average of speeds unless explicitly traveling equal time—this is the most common mistake costing 2-3 marks per exam.
Do I need to memorize all train formulas separately for RRB NTPC?
No, understand the core logic: train length matters when crossing extended objects (platforms, bridges). Add train length + object length, divide by speed. For point objects (poles, standing people), use only train length. For two trains, add both lengths. Same/opposite direction rules follow relative speed formulas. This logical approach eliminates memorizing 10+ separate formulas.
How many speed, time & distance questions should I practice daily for RRB NTPC?
Practice 30-35 questions daily for 3 weeks before exam. Start with 20 questions in Week 1 (formula familiarity), increase to 30-35 in Week 2 (mixed practice), and 40-45 in Week 3 (speed building). Focus on accuracy first (target 85%+), then reduce average solving time to 50-60 seconds per question. Quality practice with formula analysis beats quantity.
Conclusion: Your Next Step
This RRB NTPC speed, time, and distance formula sheet covers every formula tested in CBT 1 and CBT 2. Focus on basic formulas, relative speed, and train problems first—these three categories contribute 75-80% of questions.
Print this formula sheet and solve 30-35 daily practice problems for three weeks. Track which formulas you confuse most frequently and drill those specifically. With systematic practice, formula recall becomes automatic, reducing your solving time to 45-60 seconds per question while maintaining 85-90% accuracy.
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