8 questions from actual SSC CGL papers · all shown free · click option to reveal solution
RELATIVE SPEED — COMPLETE GUIDE FOR SSC CGL ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
CORE CONCEPT — WHAT IS RELATIVE SPEED? ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
Imagine you are sitting in a train moving at 60 km/h. Another train passes you at 80 km/h in the same direction. From your seat, the other train feels like it is moving at just 20 km/h — not 80 km/h. This 'felt' speed is called Relative Speed. In simple words: Relative Speed is the speed of one object as seen from another moving object.
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ KEY RULES — THE TWO GOLDEN RULES
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Rule 1 — OPPOSITE DIRECTIONS:
When two objects move towards each other (or away from each other in opposite directions), their speeds ADD UP. Relative Speed = Speed A + Speed B
Rule 2 — SAME DIRECTION: When two objects move in the same direction, their speeds are SUBTRACTED.
Relative Speed = Speed A − Speed B (take the bigger minus the smaller) Memory Trick: OPPOSITE = ADD. SAME = SUBTRACT.
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— HOW IT IS ASKED ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ SSC CGL asks Relative Speed in 4 main ways: → Two trains crossing each other (most common) → A person running towards or away from a train → Two people walking towards or away from each other → Boats and streams (a special form of relative speed) In train problems, always remember: the TOTAL DISTANCE = Length of Train 1 + Length of Train 2 (when crossing each other). If a train crosses a stationary pole or person, distance = only the train's own length. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Trick 1 — TIME TO MEET SHORTCUT: If two people start from opposite ends of a road of length D km, walking at speeds u and v: Time to meet = D / (u + v) Trick 2 — TRAIN CROSSING A MOVING PERSON: If a train of length L moves at speed T and a person walks at speed P in the SAME direction: Time to cross = L / (T − P) If they move in OPPOSITE directions: Time to cross = L / (T + P) Trick 3 — FIND ORIGINAL SPEED WHEN MEETING TIME IS GIVEN: If two trains A and B start at the same time from stations X and Y towards each other and meet after time T: Speed of A / Speed of B = Distance covered by A / Distance covered by B This ratio stays constant and is extremely useful in advanced problems. ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
— TRAINS CROSSING (OPPOSITE DIRECTION) ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Question: Two trains of lengths 120 m and 80 m are moving towards each other at 60 km/h and 40 km/h. How long will they take to cross each other? Step 1 — Total distance to cover = 120 + 80 = 200 m Step 2 — Relative Speed = 60 + 40 = 100 km/h (opposite directions, so ADD) Step 3 — Convert to m/s: 100 × 5/18 = 500/18 = 27.78 m/s Step 4 — Time = Distance / Speed = 200 / (500/18) = 200 × 18/500 = 3600/500 = 7.2 seconds Answer: 7.2 seconds ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ WORKED EXAMPLE 2 — SAME DIRECTION, PERSON WALKING ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ Question: A train 150 m long runs at 54 km/h. A man runs at 18 km/h in the same direction.
In how many seconds will the train pass the man? Step 1 — Relative Speed = 54 − 18 = 36 km/h (same direction, SUBTRACT) Step 2 — Convert to m/s: 36 × 5/18 = 10 m/s Step 3 — Distance = length of train = 150 m (man is a point object) Step 4 — Time = 150 / 10 = 15 seconds Answer: 15 seconds ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ #1 MOST COMMON TRAP — DO NOT FALL FOR THIS ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ TRAP: Students forget to ADD the lengths of BOTH trains when two trains cross each other. They use only one train's length. This gives a completely wrong answer.
Always check — are both objects moving? If yes, total distance = sum of both lengths. If one object is a pole or a standing person, distance = only the moving train's length.
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