Time, Speed and Distance Questions for SSC CGL

Core Relationship and Unit Conversion

Speed is the rate at which distance is covered per unit time. The fundamental relationship is Distance = Speed × Time. In SSC CGL, questions often mix units (km/h, m/s, km/min) to test conversion skill. Remember: 1 km/h = 5/18 m/s and 1 m/s = 18/5 km/h. This conversion is tested almost every exam cycle. Always convert to consistent units before solving.

• Distance = Speed × Time (rearrange as needed)
• To convert km/h to m/s: multiply by 5/18
• To convert m/s to km/h: multiply by 18/5
• Always check units before substituting into formulas
• Speed is always positive; direction is handled separately in relative motion

Relative Speed: Trains and Objects

When two objects move, their relative speed depends on direction. If moving in same direction, relative speed = difference of speeds. If moving in opposite directions, relative speed = sum of speeds. This is the most tested concept in SSC CGL. Train problems often ask about crossing platforms, poles, or other trains. When a train crosses a pole, it travels its own length. When crossing a platform or another train, it travels its length plus the other object's length.

• Same direction: Relative Speed = S1 - S2 (faster minus slower)
• Opposite direction: Relative Speed = S1 + S2
• Train crossing pole: Distance = Length of train only
• Train crossing platform/bridge: Distance = Length of train + Length of platform
• Train crossing another train: Distance = Sum of both train lengths
• Time to cross = Distance / Relative Speed

Average Speed and Multi-Leg Journeys

Average speed is NOT the arithmetic mean of speeds. It is total distance divided by total time. This is a critical trap in SSC CGL. When someone travels different distances at different speeds, or same distance at different speeds, you must calculate total distance and total time separately. A common variant: same distance covered at two different speeds — use harmonic mean formula.

• Average Speed = Total Distance / Total Time (not average of speeds)
• For same distance at two speeds: Avg Speed = 2S1×S2 / (S1 + S2) (harmonic mean)
• For different distances: Add all distances, add all times, then divide
• Harmonic mean applies only when distances are equal
• Always verify units are consistent across all legs

Boats and Streams (Relative Speed in Fluids)

Boat problems are variations of relative speed. Downstream: boat speed + stream speed. Upstream: boat speed - stream speed. The stream adds or subtracts from the boat's effective speed. This is tested frequently in Tier 1. Key insight: if a boat takes time T1 downstream and T2 upstream for the same distance, you can set up equations to find boat speed and stream speed separately.

• Downstream speed = Boat speed + Stream speed
• Upstream speed = Boat speed - Stream speed
• Time downstream < Time upstream (for same distance)
• If speeds are given, use relative speed formula directly
• If times are given, set up equations: D = (B+S)×T1 = (B-S)×T2

• Confusing average speed with arithmetic mean of speeds. Always use Total Distance / Total Time.
• Forgetting to convert units before calculation. A 60 km/h speed and a 10 m/s speed cannot be directly compared or added without conversion.
• In train crossing problems, forgetting to add both train lengths when two trains cross each other. Only the pole case uses single train length.
• Misapplying harmonic mean formula when distances are unequal. Harmonic mean works ONLY for equal distances at different speeds.
• In boat problems, subtracting stream speed incorrectly. Upstream is always (Boat - Stream), not (Stream - Boat).

• DeST: Distance = Speed × Time. Rearrange as needed (D/S = T, D/T = S).
• SODA: Same direction = Opposite (subtract), Opposite direction = Add. Helps recall relative speed rules.
• 5/18 Magic: km/h to m/s multiply by 5/18; m/s to km/h multiply by 18/5. These are reciprocals.
• Harmonic Mean Trick: Equal distances, different speeds → use 2S1×S2/(S1+S2). Unequal distances → use Total D / Total T.
• Boats: Down = B+S, Up = B-S. Think of stream as helper (down) or obstacle (up).

• SSC CGL Tier 1 typically has 1-2 straightforward TSD questions (basic formula, unit conversion, or simple relative speed). Solve in under 90 seconds.
• Tier 2 (Maths) has 2-3 questions, often combining TSD with algebra. Expect multi-leg journeys or boat-stream problems requiring equation setup.
• Train crossing problems are almost guaranteed. Practice pole, platform, and train-crossing variants. These appear in 60% of papers.
• Average speed trap is very common. Examiners deliberately give arithmetic mean as a distractor. Always calculate Total D / Total T.
• Recent papers show increased focus on boats/streams and relative speed of two moving objects. Less emphasis on pure distance-time graphs.