Time, Speed and Distance Tricks: Trains, Boats and Streams, Relative Speed Questions for SSC CGL, CHSL
Rahul Kumar
SSC Exam Expert & Content Editor
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PDF Notes: Time, Speed and Distance Tricks: Trains, Boats and Streams, Relative Speed Questions for SSC CGL, CHSL
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Time, speed and distance (TSD) gives 3 to 5 questions in SSC CGL and CHSL maths, including the train, boat and race problems. All of them come from the formula Speed = Distance / Time and a few rules for relative speed. These time, speed and distance tricks for SSC explain the rules and solve every popular type step by step.
Basic Rules
| Rule | Formula |
|---|---|
| Speed | Distance / Time |
| km/h to m/s | Multiply by 5/18 |
| m/s to km/h | Multiply by 18/5 |
| Same distance | Speed and time are in the inverse ratio |
| Average speed (equal distances) | 2xy / (x + y) |
| Relative speed (opposite direction) | Sum of the speeds |
| Relative speed (same direction) | Difference of the speeds |
Trains
| Case | Time taken |
|---|---|
| Train crosses a pole or a man | Length of the train / Speed |
| Train crosses a platform or a bridge | (Train + platform length) / Speed |
| Two trains in opposite directions | (L1 + L2) / (S1 + S2) |
| Two trains in the same direction | (L1 + L2) / (S1 − S2) |
Boats and Streams
| Item | Formula |
|---|---|
| Downstream speed | Boat + stream |
| Upstream speed | Boat − stream |
| Boat in still water | (Downstream + Upstream) / 2 |
| Stream | (Downstream − Upstream) / 2 |
Solved Examples
Example 1. Convert 54 km/h into m/s.
54 × 5/18 = 15 m/s.
Example 2. A train 150 m long crosses a platform 250 m long at 72 km/h. Find the time.
72 km/h = 20 m/s. Time = (150 + 250)/20 = 20 seconds.
Example 3. Two trains of length 125 m and 175 m run in opposite directions at 50 km/h and 40 km/h. In how much time do they cross each other?
Relative speed = 90 km/h = 25 m/s. Time = 300/25 = 12 seconds.
Example 4. A boat goes downstream at 15 km/h and upstream at 9 km/h. Find the speed of the boat and of the stream.
Boat = (15 + 9)/2 = 12 km/h, stream = (15 − 9)/2 = 3 km/h.
Example 5. A man goes from A to B at 30 km/h and returns at 20 km/h. Find the average speed.
2 × 30 × 20/(30 + 20) = 24 km/h.
Example 6. Two persons start from two points 36 km apart and walk towards each other at 5 km/h and 7 km/h. When do they meet?
36/(5 + 7) = 3 hours.
Example 7 (race). A runs 100 m in 20 s and B runs 100 m in 25 s. By how many metres does A win?
In 20 s, B runs 100/25 × 20 = 80 m. A wins by 20 m.
Quick Tips
- Convert all units into km/h or m/s first.
- For trains add the lengths when the train crosses another long thing.
- Use 2xy/(x + y) only for equal distances.
- Draw a small line diagram for meeting questions.
Quick Revision Points
- km/h × 5/18 = m/s.
- Opposite direction: add the speeds.
- Same direction: subtract the speeds.
- Boat in still water = (D + U)/2.
- Average speed for equal distances = 2xy/(x + y).
Practice Questions With Answers
- Convert 90 km/h into m/s.
Answer: 25 m/s - Convert 20 m/s into km/h.
Answer: 72 km/h - A 200 m train at 36 km/h crosses a pole. Find the time.
Answer: 20 seconds - A 300 m train at 54 km/h crosses a 300 m platform. Find the time.
Answer: 40 seconds - A boat goes at 8 km/h in still water and the stream is 2 km/h. Find the upstream speed.
Answer: 6 km/h - The downstream speed is 20 km/h and the upstream speed is 10 km/h. Find the stream speed.
Answer: 5 km/h - Find the average speed for equal distances at 60 km/h and 40 km/h.
Answer: 48 km/h - Two trains of 150 m and 100 m run in opposite directions at 36 and 54 km/h. Find the time to cross.
Answer: 10 seconds - A car covers 120 km in 3 hours. How long for 200 km at the same speed?
Answer: 5 hours - If the speed increases by 25%, by how much does the time change?
Answer: It decreases by 20%
How to Practise This Chapter
Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Mathematics notes page, read the previous topic Time and Work Tricks and the next topic Number System Tricks. Formulas are in the Formula Guide and more practice is in the Quantitative Aptitude notes. Also read the Time, Speed and Distance Formula Guide.
Frequently Asked Questions
What is the formula for speed?
Speed = Distance / Time.
How do I convert km/h to m/s?
Multiply by 5/18.
What is relative speed?
It is the speed of one object as seen from another: the sum in opposite directions and the difference in the same direction.
How long does a train take to cross a platform?
(Length of the train + length of the platform) / speed.
What are downstream and upstream?
Downstream is with the stream (boat + stream) and upstream is against it (boat − stream).
What is the average speed for equal distances?
2xy/(x + y).
What if the speed increases?
For the same distance, the time decreases in the inverse ratio.
Is TSD asked in SSC exams?
Yes. It is asked in every SSC maths paper.
What are common mistakes?
Not converting units and using the average of speeds instead of the harmonic formula.
How much time should I take?
About 40 to 60 seconds.
How do I find the time of meeting?
Distance divided by the sum of the speeds.
What is a dead heat?
It is a race in which all runners finish at the same time.
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Time and Work Tricks: LCM Method, Pipes and Cisterns and Wages Questions for SSC CGL, CHSL
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Number System Tricks: Divisibility, Remainder, Unit Digit, HCF and LCM Questions for SSC CGL, CHSL
Rahul Kumar
SSC Exam Expert & Content Editor
Rahul is a senior SSC exam strategist with 8+ years of experience helping aspirants crack CGL, CHSL and MTS exams. He writes in-depth notification breakdowns, exam pattern guides and preparation strategies.