The distance between two cities A and B is 200 km. A bus starts from city A at 7 a.m. and travels towards city B at 20 km per hour. Another bus starts from city B at 8 a.m. and travels towards city A at 25 km per hour. They will meet at:

1. A

   110 km from city B

2. B

   105 km from city A

3. C

   120 km from city A

4. D

   100 km from city B

Appeared in: ESIC Nursing Officer 2016 (shift-1)

Explanation

• The core of this problem is calculating when and where two objects moving towards each other will meet, considering they start at different times.
• First, calculate the distance covered by Bus A in the one hour before Bus B starts: 20 km/hr × 1 hr = 20 km. The remaining distance is 200 - 20 = 180 km.
• Next, calculate their combined (relative) speed since they are moving towards each other: 20 km/hr + 25 km/hr = 45 km/hr.
• The time it takes for them to cover the remaining 180 km is: Time = Distance / Speed = 180 km / 45 km/hr = 4 hours.
• Finally, calculate the distance from City B where they meet. Bus B travels for 4 hours at 25 km/hr: Distance = 25 km/hr × 4 hr = 100 km.

Why Other Options Were Wrong

• Option A: This value would be incorrect. It may result from miscalculating the time to meet or using the wrong speed in the final calculation.
• Option B: This value is incorrect. The distance from city A is 100 km, not 105 km. This error could arise from a slight miscalculation in time or speed.
• Option C: This value is incorrect. The distance from city A is 100 km. This might be calculated by incorrectly adding the initial 20 km head start to the distance Bus B traveled (20 + 100 = 120), which is a flawed method.

Related Visual

• Visual 1: Diagram - A line representing the 200 km distance between City A and City B. Arrows can show the starting positions of Bus A and Bus B, their directions of travel, and the final meeting point marked at the 100 km mark from both cities.

Clinical Relevance

• Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain This question tests the application of concepts related to time, speed, and distance, specifically involving objects moving towards each other from different starting times (relative speed) as background academic context rather than a clinical decision trigger.
• While not a clinical question, this type of logical and mathematical reasoning is a component of general aptitude tests included in many nursing recruitment exams.
• Numeracy skills are essential for nurses for tasks like medication dosage calculation, IV drip rate monitoring, and interpreting patient data charts, making aptitude questions relevant.
• What if? - If Bus B also started at 7 a.m., they would meet sooner. The time to meet would be Total Distance / Relative Speed = 200 km / 45 km/hr = approximately 4.44 hours. The meeting point would be 4.44 hr × 20 km/hr = 88.8 km from City A.

How to Approach the Question

• First, identify all the given variables: total distance (200 km), speed of Bus A (20 km/hr), speed of Bus B (25 km/hr), and their start times (7 a.m. and 8 a.m.).
• Notice the different start times. Calculate the distance the first bus (A) covers before the second bus (B) starts. This is the 'head start'.
• Subtract the head start distance from the total distance to find the new distance between the buses when both are moving.
• Calculate the 'relative speed' by adding the speeds of the two buses because they are traveling towards each other.
• Use the formula Time = Distance / Speed to find how long it takes for them to meet from the moment the second bus starts.
• Finally, calculate the meeting point's distance from one of the cities using the time you just found and the speed of the bus that started from that city.

Concept Tested & Keywords

• Concept Tested: This question tests the application of concepts related to time, speed, and distance, specifically involving objects moving towards each other from different starting times (relative speed).
• Stem keywords: distance, cities A and B, 200 km, bus, starts, travels towards, km per hour
• Lead-in keywords: meet at

Question ID

Qhzx-g2IZlh3md0yaUGWtF

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