Speed, Distance and Time Questions for SSC CHSL

The Core Triangle

Everything in this topic comes from one relationship: Distance equals Speed multiplied by Time. Think of it as a triangle — cover the quantity you want to find, and multiply or divide the other two. This single formula is the parent of every question in this chapter.

• Distance = Speed x Time
• Speed = Distance / Time
• Time = Distance / Speed
• Units must match: if speed is in km/h, time must be in hours, distance in km
• To convert km/h to m/s: multiply by 5/18
• To convert m/s to km/h: multiply by 18/5

Average Speed — The Most Tested Trap

When an object travels the same distance at two different speeds, the average speed is NOT the simple average. It is the Harmonic Mean formula. This is the single most tested concept in CHSL SDT questions. The simple average works ONLY when time is equal, not when distance is equal.

• Same distance at speed A and B: Average Speed = 2AB / (A+B)
• Simple average (A+B)/2 is WRONG when distances are equal
• Simple average IS correct when time spent at each speed is equal
• Always ask yourself: is distance same or time same?
• If three equal distances: Average Speed = 3ABC / (AB+BC+CA)

Relative Speed — Trains and Moving Objects

When two objects move, their effective speed relative to each other depends on direction. Objects moving in the same direction subtract speeds; objects moving opposite directions add speeds. This is heavily tested in the trains sub-topic where you also need to account for the length of the train(s).

• Opposite directions: Relative Speed = S1 + S2
• Same direction: Relative Speed = S1 - S2 (larger minus smaller)
• Train crossing a pole or person: Distance = Length of train only
• Train crossing a platform or bridge: Distance = Length of train + Length of platform
• Two trains crossing each other: Distance = Sum of both lengths
• Time = Total Distance / Relative Speed

Boats and Streams

A boat in a river has two speed components: the boat's own speed (in still water) and the river's current. Going downstream (with current) the speeds add. Going upstream (against current) they subtract. CHSL regularly asks you to find boat speed or stream speed given upstream and downstream speeds.

• Downstream speed = Boat speed + Stream speed
• Upstream speed = Boat speed - Stream speed
• Boat speed in still water = (Downstream + Upstream) / 2
• Stream speed = (Downstream - Upstream) / 2
• If upstream time and downstream time are given, use D = S x T carefully

Time-Distance Ratio Shortcut

When speed changes but distance is constant, time and speed are inversely proportional. This gives a fast shortcut without calculating actual distances. CHSL often frames questions like: a person is late or early by X minutes — use this ratio trick to save time.

• Same distance: Time is inversely proportional to Speed
• If speed increases by a fraction, time decreases by inverse fraction
• If speed ratio is A:B, time ratio is B:A (for same distance)
• Useful for late/early arrival problems without knowing actual distance

• Using simple average (A+B)/2 for average speed when distances are equal — always use 2AB/(A+B) for equal distances.
• Forgetting to convert km/h to m/s (multiply by 5/18) before using metres and seconds in train problems — mismatched units kill the answer.
• In train crossing a person/pole problems, counting the person's length or adding platform length incorrectly — person/pole has zero length, platform length must be added.
• Confusing same-direction and opposite-direction relative speed — same direction means subtract, opposite means add. A classic exam trap.
• In boats and streams, mixing up which formula gives boat speed and which gives stream speed — remember B = (D+U)/2 and S = (D-U)/2, add for boat, subtract for stream.

• DST Triangle: Draw a triangle with D on top, S and T at bottom. Cover what you want — the remaining two show multiply or divide.
• SAME direction = SUBTRACT speeds (both going same way, one barely overtakes). OPPOSITE = ADD (head-on collision has more impact). Think road safety: head-on is more dangerous = bigger combined speed.
• Boats: Downstream is like going WITH the crowd (add), Upstream is AGAINST the crowd (subtract). Average = middle point = (D+U)/2.
• 5/18 shortcut: Remember 5 and 18 by thinking 5 fingers, 18 is 5+13 — or just remember the phrase 'Fifty-eighteen, km to m scene' for km/h to m/s conversion.

• CHSL typically places 2-3 SDT questions in the Quant section — at least one will be average speed or trains. Expect one boats question roughly every other paper.
• Difficulty stays at easy-to-medium. If a question looks complicated, you are likely overcomplicating it — re-read and identify if it is a simple ratio problem.
• Train problems almost always require unit conversion. The moment you see a train question with metres and km/h, immediately write down the m/s conversion before doing anything else.
• Average speed questions often disguise the equal-distance condition — if a person goes and comes back, distances are always equal, so always use 2AB/(A+B).
• For late/early arrival problems, set up the ratio method rather than algebra. It is 3x faster and reduces calculation errors under exam pressure.