Overtaking time with staggered starts: Arun starts from P at 6:00 am at 8 km/h. Bhaskar starts from P at 7:30 am at 12 km/h, both running in the same direction. At what time does Bhaskar overtake Arun?
Aptitude
Races and Games
Difficulty: Easy
Choose an option
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A10 : 30 am
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B9 : 00 am
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C11 : 30 am
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D1 : 00 am
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ENone of these
Answer
Correct Answer: 10 : 30 am
Explanation
Introduction / Context:Overtaking with different start times uses relative speed and initial lead distance acquired before the faster runner starts.
Given Data / Assumptions:
- Arun: 8 km/h from 6:00 am.
- Bhaskar: 12 km/h from 7:30 am (1.5 h later).
- Same route and direction; constant speeds.
Concept / Approach:Lead distance at 7:30 am is d = 8 * 1.5 = 12 km. Relative speed = 12 − 8 = 4 km/h. Catch time after 7:30 am is d / relative speed.
Step-by-Step Solution:
Lead at 7:30 am = 12 kmRelative speed = 4 km/hCatch time = 12 / 4 = 3 hOvertake time = 7:30 am + 3 h = 10:30 amVerification / Alternative check:Distances by 10:30 am: Arun = 4.5 h * 8 = 36 km; Bhaskar = 3 h * 12 = 36 km – same point.
Why Other Options Are Wrong:9:00/11:30 do not satisfy both distances equally; 1:00 am is nonsensical in this context.
Common Pitfalls:Forgetting to compute Arun’s initial lead before Bhaskar starts.
Final Answer:10 : 30 am