Practice Questions
Concept Explanation
Relative speed is the speed of one moving object as seen from another moving object.
Key Formulas
- Same direction: relative speed = |a − b|
- Opposite direction: relative speed = a + b
- Time to meet or cross = Total distance / Relative speed
Example
Two cars at 60 km/h and 40 km/h approach each other. Relative speed = 60 + 40 = 100 km/h.
Common Trap
Subtract speeds only when moving in the same direction. Add when moving toward each other.
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Q1 Easy
Two cars travel toward each other at speeds of 60 km/h and 40 km/h respectively. What is their relative speed?
ExplanationOpposite direction: relative speed = 60 + 40 = 100 km/h. -
Q2 Easy
Two vehicles move in the same direction at 90 km/h and 60 km/h respectively. What is their relative speed?
ExplanationSame direction: relative speed = |90 − 60| = 30 km/h. -
Q3 Medium
Two persons A and B move toward each other at 50 km/h and 30 km/h respectively. If they meet after 2 hours, what was the initial distance between them?
ExplanationRelative speed = 80 km/h. Initial gap = 80 × 2 = 160 km. -
Q4 Easy
Two runners move in the same direction at 12 m/s and 8 m/s respectively. At what rate does the faster runner gain on the slower runner?
ExplanationRelative speed = 12 − 8 = 4 m/s. -
Q5 Easy
Two trains, each moving at 72 km/h, travel toward each other on parallel tracks. What is their relative speed?
ExplanationOpposite direction: relative speed = 72 + 72 = 144 km/h. -
Q6 Medium
Car A travels at 80 km/h and chases Car B, which moves at 60 km/h in the same direction. If B is 40 km ahead of A, after how many hours will A catch B?
ExplanationRelative speed = 20 km/h. Time = 40 ÷ 20 = 2 hours. -
Q7 Medium
Two cyclists start from opposite ends of a 210 km route and ride toward each other at 18 km/h and 24 km/h respectively. After how many hours will they meet?
ExplanationRelative speed = 42 km/h. Time = 210 ÷ 42 = 5 hours.
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Q8 Easy
Two boats move in the same direction at 15 km/h and 10 km/h respectively. What is their relative speed?
ExplanationSame direction: relative speed = 15 − 10 = 5 km/h. -
Q9 Medium
Two objects move toward each other, each at 45 km/h. If the initial distance between them is 225 km, after how many hours will they meet?
ExplanationRelative speed = 90 km/h. Time = 225 ÷ 90 = 2.5 hours. -
Q10 Hard
Object A moves at 20 m/s and Object B at 14 m/s in the same direction. If A is 60 m behind B, how many seconds will A take to catch B?
ExplanationRelative speed = 6 m/s. Time = 60 ÷ 6 = 10 s. -
Q11 Easy
Two cars travel toward each other at 55 km/h and 65 km/h respectively. What is their relative speed?
ExplanationOpposite direction: relative speed = 55 + 65 = 120 km/h. -
Q12 Easy
Two vehicles move in the same direction at 100 km/h and 70 km/h respectively. At what rate does the gap between them close?
ExplanationRelative speed = 100 − 70 = 30 km/h. -
Q13 Medium
Two trains are 300 km apart and move toward each other at 50 km/h and 70 km/h respectively. After how many hours will they meet?
ExplanationRelative speed = 120 km/h. Time = 300 ÷ 120 = 2.5 hours. -
Q14 Hard
Which pair of speeds gives a relative speed of 50 km/h when both objects move in the same direction?
Explanation|80 − 30| = 50 km/h.
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DS1 Easy
What is the relative speed of the two objects?
Statement ITwo objects move toward each other at speeds of 60 km/h and 40 km/h respectively.
Statement IITwo objects move in the same direction at speeds of 60 km/h and 40 km/h respectively.
ExplanationStatement I alone: 60 + 40 = 100 km/h. Statement II alone: 60 − 40 = 20 km/h. -
DS2 Easy
After how many hours will the two objects meet?
Statement IThe initial distance between them is 160 km.
Statement IITheir relative speed is 80 km/h.
ExplanationBoth statements are needed: time = 160 ÷ 80 = 2 hours.
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DS3 Medium
Is the relative speed of the two objects greater than 100 km/h?
Statement IThe objects move toward each other at 55 km/h and 65 km/h respectively.
Statement IIThe objects move in the same direction at 90 km/h and 60 km/h respectively.
ExplanationStatement I alone: 120 km/h > 100. Statement II alone: 30 km/h, which is not sufficient. -
DS4 Easy
What was the initial distance between the two objects?
Statement IThey meet after 2 hours.
Statement IITheir relative speed is 50 km/h.
ExplanationBoth statements are needed: distance = 50 × 2 = 100 km.