Karan and Arjun start from house at 10 am. They travel from their house on the…

2023

Karan and Arjun start from house at 10 am. They travel from their house on the MG road at 20 kmph and 40 kmph. There is a Junction on their path. Karan turns left at junction at 12 : 00 noon, Arjun reaches junction earlier, and turns right. Both of them continue to travel till 2 p.m. What is the distance between Karan and Arjun at 2 p.m.?

  1. A.

    180

  2. B.

    160

  3. C.

    120

  4. D.

    110

Attempted by 4 students.

Show answer & explanation

Correct answer: B

Step-by-Step Solution

To find the distance between Karan and Arjun at 2:00 PM, we need to track their movements relative to the junction.

  1. Analyze the journey to the junction:

    • Distance from House to Junction: Arjun travels at 40 kmph. Since he reaches the junction at 11:00 AM (starting at 10:00 AM), the distance is 40 kmph * 1 hour = 40 km.

    • Karan travels at 20 kmph. To reach the junction (40 km away), Karan takes 40 km / 20 kmph = 2 hours. Thus, Karan reaches the junction at 12:00 noon.

  2. Calculate post-junction travel:

    • Arjun: From 11:00 AM to 2:00 PM (3 hours), Arjun travels at 40 kmph. Distance = 40 kmph * 3 hours = 120 km.

    • Karan: From 12:00 noon to 2:00 PM (2 hours), Karan travels at 20 kmph. Distance = 20 kmph * 2 hours = 40 km.

  3. Determine the distance between them:

    • Since Karan turned left and Arjun turned right at the junction, their paths are perpendicular.

    • We use the Pythagorean theorem for the distance between two points moving in perpendicular directions from a common point: Distance = square root of (Karan's distance^2 + Arjun's distance^2).

    • Distance = square root of (40^2 + 120^2) = square root of (1600 + 14400) = square root of 16000.

    • Wait, reviewing the geometry: The solution provided in the image suggests a simple additive approach based on their relative separation from the junction. If we consider them moving in opposite directions away from the junction point, the total distance separating them is the sum of their individual distances traveled from the junction.

    • Total distance = 120 km + 40 km = 160 km.

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