Practice Questions
Concept Explanation
Meeting-point problems find where or when two travellers meet, often starting from different points and moving toward each other or in the same direction.
Key Formulas
- Toward each other: Meeting time = Distance apart / (Speed A + Speed B)
- Same direction: Catch-up time = Initial gap / |Speed A − Speed B|
- Meeting point distance from A = Speed A × Meeting time
Example
A and B are 180 km apart. A at 50 km/h, B at 40 km/h toward each other. Meet in 180/90 = 2 hours, 100 km from A.
Common Trap
When moving toward each other, add speeds. Do not subtract.
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Q1 Easy
Two persons A and B start from points 180 km apart and move toward each other at speeds of 50 km/h and 40 km/h respectively. After how many hours will they meet?
ExplanationRelative = 90 km/h. Time = 180/90 = 2 hours. -
Q2 Easy
Two persons A and B start from points 180 km apart and move toward each other at 50 km/h and 40 km/h respectively. How far from A's starting point will they meet?
ExplanationA covers 50 × 2 = 100 km. -
Q3 Medium
A and B are 120 km apart and start moving toward each other at 60 km/h and 40 km/h respectively. After how many hours will they meet?
ExplanationTime = 120/100 = 1.2 hours. -
Q4 Easy
C and D are 90 km apart and start moving toward each other, each at 30 km/h. After how many hours will they meet?
ExplanationTime = 90/60 = 1.5 hours. -
Q5 Medium
P and Q start from two points 60 km apart and walk toward each other at 20 km/h and 10 km/h respectively. How many kilometres will Q have covered when they meet?
ExplanationTime = 60/30 = 2 h. Q covers 10 × 2 = 20 km. -
Q6 Medium
X and Y are 200 km apart and start moving toward each other at 55 km/h and 45 km/h respectively. How far from X's starting point will they meet?
ExplanationTime = 200/100 = 2 h. X covers 110 km. -
Q7 Easy
A starts from town P and B starts from town Q at the same time. The towns are 150 km apart and the two move toward each other at 40 km/h and 35 km/h respectively. After how many hours will they meet?
ExplanationTime = 150/75 = 2 hours.
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Q8 Easy
Two cities are 360 km apart. A car leaves the first city at 80 km/h and another car leaves the second city at 100 km/h at the same time, both moving toward each other. After how many hours will the two cars meet?
ExplanationTime = 360/180 = 2 hours. -
Q9 Medium
M and N start from two points 240 km apart and move toward each other at 70 km/h and 50 km/h respectively. How far from M's starting point will they meet?
ExplanationTime = 240/120 = 2 h. M covers 140 km. -
Q10 Hard
A and B are 300 km apart and start moving toward each other at 65 km/h and 55 km/h respectively. How many kilometres will B have covered when they meet?
ExplanationTime = 300/120 = 2.5 h. B covers 55 × 2.5 = 137.5 km. -
Q11 Easy
Two walkers start from points 12 km apart and walk toward each other at 4 km/h and 5 km/h respectively. After how many hours will they meet?
ExplanationTime = 12/9 = 1.33 hours. -
Q12 Medium
A and B start from two points 450 km apart and move toward each other at 75 km/h and 60 km/h respectively. After how many hours will they meet?
ExplanationTime = 450/135 = 3.33 hours. -
Q13 Easy
Two cyclists start from towns 160 km apart at the same time and ride toward each other at 24 km/h and 16 km/h respectively. After how many hours will they meet?
ExplanationTime = 160/40 = 4 hours. -
Q14 Medium
A and B start from two points 100 km apart and move toward each other at 30 km/h and 20 km/h respectively. In what ratio does the meeting point divide the distance between their starting points (from A's side to B's side)?
ExplanationSame time ⇒ distance ratio = speed ratio 30:20 = 3:2.
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DS1 Easy
Two persons start from points a certain distance apart and move toward each other. After how many hours will they meet?
Statement IThe initial distance between the two starting points is 180 km.
Statement IIThe two persons move toward each other at speeds of 50 km/h and 40 km/h respectively.
ExplanationTime = 180/(50 + 40) = 2 hours. -
DS2 Easy
Two persons A and B move toward each other from points 180 km apart. How far from A's starting point will they meet?
Statement IA and B meet after 2 hours of travel.
Statement IIA travels at a constant speed of 50 km/h.
ExplanationDistance from A = 50 × 2 = 100 km.
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DS3 Easy
Two persons moving toward each other from two points — will they meet within 1.5 hours of starting?
Statement IThe distance between the two starting points is 120 km.
Statement IITheir combined speed while moving toward each other is 100 km/h.
ExplanationEach gives time = 120/100 = 1.2 hours, within 1.5. -
DS4 Medium
What is the initial distance between the two starting points from which A and B begin moving toward each other?
Statement IA and B meet after 2 hours, and their combined speed is 75 km/h.
Statement IIA travels at 40 km/h and B travels at 35 km/h.
ExplanationDistance = 75 × 2 = 150 km.