Time & Distance — RRB NTPC Mathematics
This topic carries roughly 9% of Mathematics's 30 questions. Every question type — trains crossing objects, boats in a stream, two people meeting or one catching up to the other — is a direct application of speed = distance/time, once the correct total distance and relative speed are identified.
1. What RRB NTPC actually asks
Expect direct speed/distance/time calculations, unit conversion between km/h and m/s, trains crossing platforms or other trains, boats and streams (downstream/upstream), and problems involving two people meeting or one catching up to another.
2. The core formula and unit conversion
Speed = distance / time. To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5. This conversion factor is worth memorising as a single number — re-deriving it from 1000m/3600s under time pressure is where the inversion error usually creeps in.
3. Trains crossing objects
When a train crosses a platform, bridge, or another stationary/moving object, the distance covered equals the sum of the train's own length and the object's length (if the object has length) — not just the train's length alone.
When two trains cross each other, moving in opposite directions, use the sum of their speeds as the relative speed; moving in the same direction, use the difference.
4. Boats and streams
Downstream speed (with the current) = boat's speed + current's speed. Upstream speed (against the current) = boat's speed − current's speed.
5. Average speed for equal distances
When a journey covers equal distances at two different speeds a and b, the average speed for the whole journey is 2ab/(a+b) — the harmonic mean, NOT the simple average (a+b)/2. This distinction matters because more time is spent at the slower speed.
Worked examples
Q1. A train 150 metres long crosses a platform 250 metres long in 20 seconds. What is the train's speed in km/h?
Pick an option to check your answer.
Show explanation
Solution. To cross the platform, the train covers its own length plus the platform's length: 150 + 250 = 400 metres in 20 seconds. Speed = 400/20 = 20 m/s.
Converting to km/h: 20 × 18/5 = 72 km/h. A common error is using only the train's length (150m) or only the platform's length (250m), forgetting to add both. Answer: (b).
Q2. A boat's speed in still water is 15 km/h, and the speed of the current is 3 km/h. How long will the boat take to travel 36 km downstream?
Pick an option to check your answer.
Show explanation
Solution. Downstream speed = boat's speed + current's speed = 15 + 3 = 18 km/h. Time = distance/speed = 36/18 = 2 hours.
A common error is using the upstream speed (15−3=12 km/h) instead, which would give 3 hours — always check the direction (downstream adds the current, upstream subtracts it) before dividing. Answer: (b).
7. Common traps
- Using only one length when a train crosses a platform or another train. Always add both lengths (train's own length plus the object's length).
- Adding speeds when trains move in the same direction, or subtracting when they move toward each other. It's the reverse: same direction uses the DIFFERENCE, opposite directions use the SUM.
- Forgetting or inverting the km/h-to-m/s conversion factor (5/18). Memorise it as a fixed number rather than re-deriving it under time pressure.
- Averaging two speeds directly instead of using the harmonic mean for equal-distance average-speed problems — 2ab/(a+b), not (a+b)/2.
- Confusing downstream and upstream direction — downstream ADDS the current's speed to the boat's own speed; upstream SUBTRACTS it.
8. Guessing strategy
A quick unit-conversion sanity check (does the final answer's magnitude make sense in km/h versus m/s?) often catches an obviously wrong-magnitude option before any full calculation.
Summary
- Time & Distance is roughly 9% of Mathematics's 30 CBT 1 questions.
- Speed = distance/time; 1 km/h = 5/18 m/s (memorise this conversion factor cold).
- When a train crosses an object, total distance = train's length + object's length.
- Relative speed: SUM when moving toward each other or opposite directions, DIFFERENCE when moving the same direction.
- Downstream = boat + current; upstream = boat − current.
- Average speed for equal distances at two speeds a, b is the harmonic mean 2ab/(a+b), not the simple average.
