Time, Speed & Distance
🔒 Log in to trackTrains, relative speed, boats & streams, average-speed traps and races — two dependable slots per Tier 1 shift and more in Tier 2. Everything hangs on D = S×T, the 5/18 conversion, and the add/subtract rule for relative speed.
One page per subtopic: detailed notes, every question type, formulas, tricks and practice sets.
Every formula on one printable page, grouped by subtopic.
5 exam-level questions worked step by step.
63 questions — untimed practice or a timed test with analysis.
Track record in the exam
Questions per shift in recent SSC CGL papers.
Test difficulty mix (63 questions)
Question patterns exams keep repeating
Taken from previous-year papers. If a pattern is marked "very common", expect to see it in your exam.
Train crossing a pole or a man
very commonA train's length and speed are given. Asks the time to pass a pole, a man or a signal.
Change km/h to m/s: multiply by 5 ÷ 18.
Time = train length ÷ speed.
A 150 m train runs at 90 km/h. How long does it take to cross a pole?
90 km/h = 90 × 5 ÷ 18 = 25 m/s
Only the train's own length has to pass: 150 m
Time = 150 ÷ 25 = 6 seconds
Train crossing a platform, bridge or another train
very common"A train crosses a pole in 12 s and a platform in 30 s." Two lengths are involved.
Add the lengths that must pass. Distance = train + platform.
Use the pole time to find the train's length.
A train at 54 km/h crosses a pole in 12 s and a platform in 30 s. How long is the platform?
54 km/h = 15 m/s
Train length = 15 × 12 = 180 m
Train + platform = 15 × 30 = 450 m
Platform = 450 − 180 = 270 m
Boat in a river (with or against the stream)
very commonBoat speeds going downstream and upstream are given. Asks the stream or boat speed.
Downstream = boat + stream. Upstream = boat − stream.
Stream is half the gap between them. Boat is half the sum.
A boat goes downstream at 15 km/h and upstream at 9 km/h. Find the stream's speed.
Gap = 15 − 9 = 6
Stream = 6 ÷ 2 = 3 km/h
(Boat = (15 + 9) ÷ 2 = 12 km/h)
Two vehicles meeting or overtaking
commonTwo vehicles move towards each other or one behind the other. Asks when they meet or pass.
Coming towards each other: add the speeds.
Same direction: subtract the speeds. Then divide the gap by it.
Two towns are 100 km apart. Buses leave together towards each other at 20 km/h and 30 km/h. When do they meet?
They close the gap at 20 + 30 = 50 km/h
Gap = 100 km
Time = 100 ÷ 50 = 2 hours
Average speed of a whole trip
commonA trip goes out and comes back (or has several parts) at different speeds. Asks the average speed.
Do not average the speeds.
Average = total distance ÷ total time.
A car goes at 40 km/h and returns on the same road at 60 km/h. Find the average speed.
Take 120 km each way
Going: 120 ÷ 40 = 3 h. Return: 120 ÷ 60 = 2 h
Total: 240 km in 5 h
Average = 240 ÷ 5 = 48 km/h (not 50)
Slower or faster speed, late or early
common"Walking at ¾ of his usual speed, he is 20 minutes late."
Slower speed means more time. Speed ¾ means time ×4/3.
The extra time is the lateness.
Walking at ¾ of his usual speed, a man is 20 minutes late. What is his usual time?
Speed ¾ → time is 4/3 of usual
Extra time = ⅓ of usual time
⅓ of usual time = 20 min
Usual time = 60 minutes
Races and head starts
common"A beats B by 20 m in a 200 m race." Asks the ratio of speeds or a finish time.
When A finishes, see how far B has run.
Distances in the same time give the speed ratio.
In a 200 m race A beats B by 20 m. Find the ratio of their speeds.
A runs 200 m while B runs 200 − 20 = 180 m
Same time, so speeds match the distances
200 : 180 = 10 : 9
Changing km/h and m/s
commonA train question gives speed in km/h but length in metres (or the other way).
km/h to m/s: multiply by 5 ÷ 18.
m/s to km/h: multiply by 18 ÷ 5.
A 120 m train crosses a pole in 8 seconds. Find its speed in km/h.
Speed = 120 ÷ 8 = 15 m/s
To km/h: 15 × 18 ÷ 5
15 ÷ 5 = 3, then 3 × 18 = 54 km/h