Time, Speed and Distance Questions for CDS

The Core Relationship

Everything in this topic flows from one equation: Speed equals Distance divided by Time. Think of it as a triangle — cover the variable you want to find, and multiply or divide the remaining two. Always check units before calculating. Distance in km, Time in hours gives Speed in km/h. If time is in minutes, convert to hours by dividing by 60.

• Speed = Distance / Time
• Distance = Speed x Time
• Time = Distance / Speed
• 1 km/h = 5/18 m/s — multiply km/h by 5/18 to get m/s
• 1 m/s = 18/5 km/h — multiply m/s by 18/5 to get km/h
• Always unify units first — mixed units are the number one trap

Average Speed — The Classic Trap

When the same distance is covered at two different speeds, the average speed is NOT the arithmetic mean. It is the harmonic mean formula below. This is the single most tested concept in CDS for this topic. Aspirants who use (u+v)/2 lose the mark every time. Only use simple average if time is equal, not distance.

• If same distance at speed u then speed v: Average Speed = 2uv / (u+v)
• If same time at speed u then speed v: Average Speed = (u+v) / 2
• Total Average Speed = Total Distance / Total Time — always works, never fails
• The harmonic mean formula only applies when two equal distances are covered

Relative Speed — Two Objects Moving

When two objects move, their effective speed depends on direction. If moving in the same direction, subtract speeds. If moving in opposite directions, add speeds. Think of two cars on a highway — if both go the same way, the faster one slowly pulls ahead (small relative speed). If they face each other, they close the gap fast (large relative speed). This logic applies to trains, people, and boats.

• Opposite directions: Relative Speed = Speed A + Speed B
• Same direction: Relative Speed = |Speed A - Speed B|
• Time to meet = Distance between them / Relative Speed
• For trains crossing each other or a platform: Distance = Length of Train 1 + Length of Train 2 (or platform length)
• A train crossing a pole or a person: Distance = Length of the train only

Boats and Streams

A boat moving in water is affected by the current. Downstream means the current helps the boat, so effective speed increases. Upstream means the current resists, so effective speed decreases. The boat's own speed in still water is called its speed in still water. The stream adds or subtracts from it. CDS frequently asks you to find the speed of the boat or the stream given downstream and upstream speeds.

• Downstream speed (D) = Boat speed + Stream speed = u + v
• Upstream speed (U) = Boat speed - Stream speed = u - v
• Speed of Boat in still water = (D + U) / 2
• Speed of Stream = (D - U) / 2
• Mnemonic: DUBS — Downstream Up Boat Stream

• Using simple average (u+v)/2 for average speed when the same DISTANCE is covered — always use 2uv/(u+v) in that case
• Forgetting to add both lengths (train + platform or train + train) when calculating crossing time — only the train length counts when crossing a pole or person
• Not converting units before calculating — mixing km/h with metres leads to completely wrong answers
• Using the wrong relative speed formula — adding speeds when objects move the same direction instead of subtracting
• In boats and streams, confusing which formula gives boat speed vs stream speed — remember both use (D+U) and (D-U), just check which is divided by 2 for which

• DST Triangle: Draw a triangle with D on top, S and T at the bottom corners. Cover what you want — if you cover D, multiply S and T. If you cover S or T, divide.
• SAME direction = SUBTRACT, OPPOSITE direction = ADD — think of two people walking same way vs head-on collision
• Average Speed Trap rhyme: Same distance? Do NOT average. Use 2uv over u-plus-v.
• DUBS for Boats: Downstream = Up (add), Boat = half Sum, Stream = half Difference

• CDS papers typically have 3 to 4 questions from this topic — usually one on average speed, one on trains, and one on boats or relative speed. Expect exactly this mix.
• Questions are mostly calculation-based with clean numbers — if your answer looks like an ugly fraction, re-check unit conversion first.
• Train problems in CDS almost always involve two lengths being added — the pole-crossing variant (only train length) appears less often but is used as a distractor option.
• Boats and streams questions in recent CDS papers (2019-2023) have favoured the reverse format — given downstream and upstream times (not speeds) for the same distance. In that case, use Speed = Distance/Time first to find D and U, then apply the formula.
• Timing advice: Each TSD question should take 90 seconds max. If a question has two unknowns, set up two equations immediately — do not guess and check as it wastes time under CDS exam pressure.