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.
-
Q1 EasyA 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 EasyA 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.
-
Q3 EasyA 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.
-
Q4 EasyA 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.
-
Q5 EasyA 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.
-
Q6 EasyA 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.
-
Q7 EasyA 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.
-
Q8 EasyA 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.
-
Q9 EasyTwo 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|.
-
Q10 MediumA 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.
-
Q11 MediumA 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.
-
Q12 MediumCar 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.
-
Q13 HardA 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.
-
Q14 HardA 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.
-
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.
-
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.