Time and Distance Questions for SSC CHSL

Basic Speed-Distance-Time Relationship

The foundation of this entire topic is one triangle relationship. Speed is how fast you go, Distance is how far you go, and Time is how long it takes. If you know any two, you can find the third. Always check units — km/hr and m/s are the two common units. Convert carefully before calculating.

• Speed = Distance divided by Time
• Distance = Speed multiplied by Time
• Time = Distance divided by Speed
• To convert km/hr to m/s: multiply by 5/18
• To convert m/s to km/hr: multiply by 18/5
• If speed doubles, time becomes half for same distance — inverse relationship

Average Speed

This is a favourite trap in SSC CHSL. If a person travels two equal distances at different speeds, average speed is NOT the simple average of the two speeds. It is the Harmonic Mean formula given below. Students who use (S1+S2)/2 will always get the wrong answer. Use the correct formula every time.

• Average Speed when equal distances at S1 and S2: use 2S1S2 / (S1+S2)
• Average Speed when equal times at S1 and S2: use (S1+S2) / 2 — this is the only case where simple average works
• Always check whether equal DISTANCE or equal TIME is given
• Average speed is always less than the arithmetic mean when distances are equal
• Total Distance divided by Total Time always gives correct average speed regardless of the situation

Trains — Crossing and Overtaking

Train questions are very common in SSC CHSL. The key idea is: when a train crosses an object, the distance covered equals the length of the train plus the length of the object. If crossing a pole or person, only train length matters. If two trains move in same direction, subtract their speeds. If they move in opposite directions, add their speeds.

• Train crossing a pole or standing person: Distance = Length of train only
• Train crossing a platform or bridge: Distance = Length of train + Length of platform
• Train crossing another train (opposite direction): Relative Speed = S1 + S2, Distance = L1 + L2
• Train crossing another train (same direction): Relative Speed = S1 - S2, Distance = L1 + L2
• Always convert speed to m/s when length is given in metres
• Time = Total Distance / Relative Speed

Boats and Streams

Boats and Streams is essentially relative speed in water. When a boat moves downstream (with the current), the current helps it go faster. When it moves upstream (against the current), the current slows it down. Let boat speed in still water = B and stream speed = S. These two formulas are all you need.

• Downstream speed = B + S (current helps the boat)
• Upstream speed = B - S (current fights the boat)
• Boat speed in still water = (Downstream + Upstream) / 2
• Stream speed = (Downstream - Upstream) / 2
• If a person swims in a river, treat exactly like boat problems
• Time ratio for same distance: Downstream time is less, Upstream time is more

Meeting Point and Relative Speed

When two people or vehicles start from two ends and move towards each other, they meet at a point. The key idea is that they together cover the total distance. When they move in the same direction, the faster one covers extra distance equal to the gap. Time to meet = Total Distance divided by Combined Speed (if opposite) or Speed Difference (if same direction).

• Moving towards each other: Time to meet = Distance / (S1 + S2)
• Moving in same direction: Time to meet = Distance / (S1 - S2)
• Distances covered by each person at meeting point are in the ratio of their speeds
• After meeting, they swap the remaining distances — useful in back-and-forth problems
• Circular track: they meet every (Track Length / Relative Speed) seconds

• Using simple average for average speed when distances are equal — this is the most common error. Always use 2S1S2/(S1+S2) for equal distance case.
• Forgetting to convert km/hr to m/s in train problems when length is given in metres. The answer goes completely wrong without this step.
• Adding only the train length instead of train+platform length when crossing a platform. A pole has zero length, a platform has its own length.
• Confusing same direction with opposite direction for relative speed of trains — same direction means subtraction, opposite means addition.
• In boats problems, confusing which formula gives boat speed and which gives stream speed. Remember: boat = sum/2, stream = difference/2.

• DST Triangle: Draw a triangle with D on top, S and T at the bottom. Cover the one you want to find. D over ST means D=SxT. S and T side by side means S=D/T and T=D/S.
• FOR CONVERSION remember FIVE-EIGHTEEN: km/hr to m/s multiply by 5/18. Think '5 fingers, 18 wheels of a truck'. Reverse for m/s to km/hr: multiply 18/5.
• BOATS: think of D and U as brothers. Add them and halve to get Boat speed (they cooperate). Subtract and halve to get Stream speed (the difference between them).
• TRAINS direction rule: SAME direction = SUBTRACT speeds (they slow down relative to each other). OPPOSITE direction = ADD speeds (they rush at each other). Think: friends walk together slowly, enemies rush at each other fast.

• SSC CHSL typically asks 2-3 questions from this topic. Boats and Trains each appear at least once in most papers. Average speed is a favourite single-question trap.
• Difficulty is mostly easy to moderate. If you see a question taking more than 90 seconds, use options. Plugin answer choices back into the formula instead of solving from scratch.
• Unit conversion is tested implicitly — they deliberately give km/hr with metres, or m/s with km. Build a reflex to check units before solving.
• Ratio shortcut: at meeting point, ratio of distances covered equals ratio of speeds. This saves full calculation in many questions.
• In recent CHSL papers (2023-2024), circular track meeting problems and train-crossing-train problems have appeared. These are medium difficulty but formula is same — just apply relative speed correctly.