SSC GD · Bite-size lessons

Time and Distance

About 7 min · Elementary Mathematics · English

Time worked out from the lesson's 459 words at 150 words a minute, plus a minute for each question.

Time and Distance is a core topic in SSC GD Elementary Mathematics. The topic tests your ability to convert units, apply the fundamental formula, and handle relative motion scenarios. Mastering this section gives you quick marks because once you learn the standard patterns, most problems solve in under 60 seconds.

Key ideas

• Fundamental Relationship: Distance = Speed × Time. Every problem boils down to finding one quantity when the other two are known.
• Unit Conversion: 1 km/h = 5/18 m/s. Multiply km/h by 5/18 to get m/s; multiply m/s by 18/5 to get km/h. Trains and platform problems almost always need m/s.
• Average Speed: When distances are equal, average speed = 2xy/(x+y) where x and y are the two speeds. When times are equal, average speed is the simple arithmetic mean (x+y)/2. Never just average speeds blindly.
• Relative Speed: When two objects move in the same direction, relative speed = |Speed₁ − Speed₂|. When moving toward each other (opposite directions), relative speed = Speed₁ + Speed₂.
• Train Problems: Length of train matters. Time to cross a pole/man = (Length of train) / (Speed of train). Time to cross a platform = (Length of train + Length of platform) / (Speed of train).

Watch out for

• Mistake: Averaging speeds as (x+y)/2 when distances are equal. Fix: Use the harmonic mean formula 2xy/(x+y) for equal distances. Simple arithmetic mean applies only when times are equal.
• Mistake: Forgetting to convert km/h to m/s in train problems. Fix: Train lengths are in metres and time in seconds, so always convert speed to m/s using ×5/18. Forgetting this step leads to wrong numerical answers.
• Mistake: Adding train lengths when a train crosses a stationary object (pole, man). Fix: When crossing a pole or man, use only the train's length. Add platform/bridge length only when the train crosses a platform or bridge.

Quick reference

• D = S × T — Distance equals speed times time. All problems stem from this.
• km/h to m/s: ×5/18 — Essential for train problems with lengths in metres.
• Average speed (equal D): 2xy/(x+y) — Not the arithmetic mean when distances are equal.
• Relative speed: same direction subtract, opposite direction add.
• Train + pole: use train length only; train + platform: add both lengths.

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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