Practice Questions
Concept Explanation
Overtaking occurs when a faster object catches a slower one moving in the same direction. The faster must cover the initial gap at relative speed.
Key Formulas
- Overtaking time = Initial gap / (Faster speed − Slower speed)
- Distance covered by faster = Faster speed × Time
- For trains: total distance to cross = sum of lengths
Example
A car at 80 km/h follows another at 60 km/h, 40 km behind. Catch-up time = 40/(80−60) = 2 hours.
Common Trap
Use difference of speeds, not sum, when chasing in the same direction.
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Q1 Easy
A car travelling at 80 km/h starts chasing another car B that is 40 km ahead and moving at 60 km/h in the same direction. After how many hours will A catch up with B?
ExplanationRelative = 20 km/h. Time = 40/20 = 2 hours. -
Q2 Medium
A car travelling at 80 km/h starts chasing another car B that is 40 km ahead and moving at 60 km/h in the same direction. How many kilometres will A travel before catching B?
ExplanationA travels 80 × 2 = 160 km. -
Q3 Medium
A car moving at 90 km/h follows another car moving at 70 km/h in the same direction. The slower car is 50 km ahead when the faster car starts. After how many hours will the faster car overtake the slower one?
ExplanationRelative = 20 km/h. Time = 50/20 = 2.5 hours. -
Q4 Easy
A runner moving at 12 m/s chases another runner moving at 9 m/s in the same direction. The slower runner is 60 metres ahead. After how many seconds will the faster runner catch up?
ExplanationRelative = 3 m/s. Time = 60/3 = 20 s. -
Q5 Easy
A bus travelling at 54 km/h follows another bus travelling at 36 km/h in the same direction. The second bus is 27 km ahead. After how many hours will the first bus overtake the second?
ExplanationRelative = 18 km/h. Time = 27/18 = 1.5 hours. -
Q6 Easy
A cyclist moving at 20 km/h chases another cyclist moving at 15 km/h in the same direction. The slower cyclist is 10 km ahead. After how many hours will the faster cyclist catch up?
ExplanationRelative = 5 km/h. Time = 10/5 = 2 hours. -
Q7 Hard
A train 150 metres long moving at 90 km/h overtakes another train 100 metres long moving at 54 km/h in the same direction. How many seconds will it take for the first train to completely pass the second?
ExplanationRelative = 36 km/h = 10 m/s. Distance = 250 m. Time = 250/10 = 25 s.
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Q8 Medium
Car A moving at 100 km/h is 30 km behind car B moving at 85 km/h in the same direction. After how many hours will A catch up with B?
ExplanationRelative = 15 km/h. Time = 30/15 = 2 hours. -
Q9 Easy
A motorcycle moving at 75 km/h follows a car moving at 60 km/h in the same direction. The car is 45 km ahead when the motorcycle starts. After how many hours will the motorcycle overtake the car?
ExplanationRelative = 15 km/h. Time = 45/15 = 3 hours. -
Q10 Easy
A faster car gains 10 km on a slower car every hour while both move in the same direction. If the slower car is initially 50 km ahead, after how many hours will the faster car overtake it?
ExplanationTime = 50/10 = 5 hours. -
Q11 Easy
A moves at 15 m/s and B moves at 12 m/s in the same direction. B is 90 metres ahead of A when A starts chasing. After how many seconds will A catch up with B?
ExplanationRelative = 3 m/s. Time = 90/3 = 30 s. -
Q12 Easy
A truck moving at 48 km/h follows another truck moving at 40 km/h in the same direction. The second truck is 32 km ahead. After how many hours will the first truck overtake the second?
ExplanationRelative = 8 km/h. Time = 32/8 = 4 hours. -
Q13 Hard
A moves at 55 km/h and B moves at 40 km/h in the same direction. B is 30 km ahead of A when A starts. How many kilometres must A travel before catching B?
ExplanationTime = 30/15 = 2 h. A travels 55 × 2 = 110 km. -
Q14 Easy
Two objects move in the same direction along a straight path. Which of the following correctly gives their relative speed?
ExplanationSame direction: relative speed = |a − b|.
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DS1 Easy
A and B move in the same direction along a straight road. After how many hours will A catch up with B?
Statement IWhen A starts, B is 40 km ahead of A.
Statement IIA travels at 80 km/h and B travels at 60 km/h.
ExplanationTime = 40/(80 − 60) = 2 hours. -
DS2 Easy
A chases B along a straight road in the same direction. How many kilometres does A travel before catching B?
Statement IA catches up with B after 2 hours.
Statement IIA travels at a constant speed of 80 km/h.
ExplanationDistance = 80 × 2 = 160 km.
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DS3 Easy
A faster vehicle follows a slower one moving in the same direction. Will the faster vehicle overtake the slower one in less than 2 hours?
Statement IThe initial gap between the two vehicles is 50 km and their relative speed is 20 km/h.
Statement IIThe faster vehicle moves at 90 km/h, the slower at 70 km/h, and the gap is 50 km.
ExplanationEach gives time = 50/20 = 2.5 hours, not less than 2. -
DS4 Easy
Two vehicles move in the same direction along a straight road. What is the initial gap between them when the faster vehicle starts chasing?
Statement IThe faster vehicle takes 2 hours to catch up with the slower one.
Statement IIThe relative speed of the two vehicles is 15 km/h.
ExplanationGap = 15 × 2 = 30 km.