In this guide
Everything in this topic comes from one relation: distance = speed × time. What makes questions hard is not the formula but the setup — what "relative speed" means when two trains pass each other, why average speed isn't the average of speeds, and how a river's current helps a boat one way and hinders it the other. Get the setup right and the arithmetic is simple.
Units
- To convert km/h to m/s, multiply by 5/18.
- To convert m/s to km/h, multiply by 18/5.
Example: 72 km/h = 72 × 5/18 = 20 m/s.
Proportionality
- At constant speed, distance ∝ time.
- For a fixed distance, speed ∝ 1/time.
Worked example: A person walking at 4/5 of their usual speed reaches 15 minutes late. Find the usual time.
New time = 5/4 × usual time, so the extra 1/4 of the usual time = 15 min. Usual time = 60 minutes.
Average speed
Average speed = total distance ÷ total time — never the simple average of speeds.
For equal distances at speeds x and y:
Average speed = 2xy/(x + y)
Worked example: A car goes from A to B at 40 km/h and returns at 60 km/h. Average speed = 2 × 40 × 60/100 = 48 km/h.
Relative speed
| Direction | Relative speed |
|---|---|
| Opposite | Sum of speeds |
| Same | Difference of speeds |
Worked example: Two cars start 300 km apart and move towards each other at 55 km/h and 45 km/h. When do they meet?
Relative speed = 100 km/h; time = 3 hours.
Trains
| Situation | Distance to cover |
|---|---|
| Crossing a pole or person | Length of the train |
| Crossing a platform or bridge | Train length + platform length |
| Crossing another train | Sum of both lengths |
Worked example: A 180 m train at 54 km/h crosses a 270 m platform. How long does it take?
Speed = 54 × 5/18 = 15 m/s. Distance = 450 m. Time = 30 seconds.
Worked example: Two trains of 120 m and 180 m run in opposite directions at 40 km/h and 50 km/h. How long do they take to cross each other?
Relative speed = 90 km/h = 25 m/s. Distance = 300 m. Time = 12 seconds.
Boats and streams
If the boat's speed in still water is b and the stream's speed is s:
- Downstream speed = b + s
- Upstream speed = b − s
- b = (downstream + upstream)/2; s = (downstream − upstream)/2
Worked example: A boat goes 24 km downstream in 2 hours and 24 km upstream in 3 hours. Find the speed of the boat and the stream.
Downstream = 12 km/h; upstream = 8 km/h. Boat = 10 km/h; stream = 2 km/h.
Races
- "A beats B by 20 m in a 100 m race" means when A finishes 100 m, B has run 80 m. Speed ratio A : B = 5 : 4.
- "A gives B a start of 10 m" means B starts 10 m ahead.
Worked example: In a 1 km race, A beats B by 100 m. In the same race, B beats C by 100 m. By how much does A beat C?
When A runs 1,000, B runs 900. When B runs 1,000, C runs 900; so when B runs 900, C runs 810. A beats C by 190 m.
Circular tracks
Two runners on a circular track of length L, with speeds a and b:
- moving in opposite directions, they meet every L/(a + b);
- moving in the same direction, every L/(a − b).
Common traps
| Trap | Correct approach |
|---|---|
| Averaging speeds directly | Use total distance ÷ total time |
| Forgetting train length | Add lengths as required |
| Mixing units | Convert everything to m/s or km/h first |
Practice
- Convert 45 km/h to m/s.
- A train 240 m long passes a pole in 16 seconds. Find its speed in km/h.
- A person travels at 30 km/h and returns at 20 km/h over the same route. Find the average speed.
- Two trains of 150 m and 100 m run in the same direction at 72 km/h and 54 km/h. How long does the faster train take to pass the slower one?
- A boat's speed in still water is 15 km/h and the stream flows at 3 km/h. How long will it take to go 36 km upstream?
- In a 200 m race, A beats B by 40 m. What is the ratio of their speeds?
Answers: 1. 12.5 m/s. 2. 54 km/h. 3. 24 km/h. 4. 50 seconds. 5. 3 hours. 6. 5 : 4.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Staff Selection Commission website .
Get the next SSC CGL guide by email
New guides every week. No spam, unsubscribe any time.