A and B are jogging around a park's circular track which has a perimeter of 1.2 km. They start from the same point at 6:00 a.m. a…

Question

A and B are jogging around a park's circular track which has a perimeter of 1.2 km. They start from the same point at 6:00 a.m. and run in opposite directions. A's speed is 5 km/h, and B's speed is 7 km/h. At what time will they meet for the fifth time?

1. A. 6:25 AM
2. B. 6:30 AM (Correct answer)
3. C. 6:45 AM
4. D. 7:00 AM

Correct Answer

Option B — 6:30 AM

Detailed Solution & Explanation

The correct answer is 6:30 AM.

Key Points

• Running in opposite directions, their speeds add: relative speed = 5 + 7 = 12 km/h.
• They meet each time they together cover one full lap of 1.2 km:
  • Time per meeting = 1.2 ÷ 12 = 0.1 hour = 6 minutes
• The fifth meeting occurs after 5 × 6 = 30 minutes.
• Starting at 6:00 a.m., they meet for the fifth time at 6:30 AM.

Additional Information

• In the same direction the relative speed is the difference (7 − 5 = 2 km/h), so meetings would come every 36 minutes instead.
• To meet again at the starting point, compute each runner's lap time and take the LCM — a different question that is frequently paired with this one.
• Converting 0.1 hour to 6 minutes is where errors creep in; multiply hours by 60 as a separate, deliberate step.

प्रश्न (हिन्दी में)

A और B एक पार्क के गोलाकार ट्रैक पर जॉगिंग कर रहे हैं जिसकी परिधि 1.2 किमी है। वे सुबह 6:00 बजे एक ही बिंदु से दौड़ना शुरू करते हैं और विपरीत दिशाओं में दौड़ते हैं। A की गति 5 किमी/घंटा है, और B की गति 7 किमी/घंटा है। वे पाँचवीं बार किस समय मिलेंगे?

1. A. 6:25 AM
2. B. 6:30 AM
3. C. 6:45 AM
4. D. 7:00 AM