Question

Children are in pursuit of a dog whose leash has broken. Krishnarajan is directly behind the dog. Rangarajan is behind Krishnarajan. Natrajan is behind Rangarajan. Premrajan is ahead of the dog walking down the street in the opposite direction. As the children and dog pass, Premrajan turns around and joins the pursuit. He runs in behind Rangarajan. Krishnarajan runs faster and is alongside the dog on the left. Rangarajan runs faster and is alongside the dog on the right. Which child is directly behind the dog?

• A. Krishnarajan
• B. Rangarajan
• C. Natrajan
• D. Premrajan

Hint:

Redraw the line of pursuit after each move described in the passage; once the two children ahead of the last spot move to flank the dog, whoever was next in line becomes the one directly behind it.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We must track who is directly behind the dog after a sequence of position changes among the dog, Krishnarajan, Rangarajan, Natrajan, and Premrajan.

Step 2: Key Formula or Approach:
Build the line of pursuit from front (closest to the dog) to back, update it each time the passage describes a move, and read off whoever ends up directly behind the dog at the end.

Step 3: Detailed Explanation:
At the start, three children chase the dog in a line: Krishnarajan is directly behind the dog, Rangarajan is behind Krishnarajan, and Natrajan is behind Rangarajan. So the order from the dog backward is: Dog, Krishnarajan, Rangarajan, Natrajan.
Premrajan is walking toward the group from the opposite direction, so he starts out ahead of the dog. When the two groups pass each other, Premrajan turns around to join the chase. The passage says he runs in behind Rangarajan, so he slots into the line right after Rangarajan and before Natrajan. The order becomes: Dog, Krishnarajan, Rangarajan, Premrajan, Natrajan.
Next, Krishnarajan speeds up and moves alongside the dog on the left. He is no longer directly behind the dog, he is beside it.
Then Rangarajan speeds up too and moves alongside the dog on the right. He is also no longer behind the dog, he is beside it on the other side.
With both Krishnarajan and Rangarajan now flanking the dog instead of trailing it, the spot directly behind the dog is taken by whoever was next in the line. That was Premrajan, who had been placed right behind Rangarajan.

Step 4: Final Answer:
Premrajan is directly behind the dog. \[ \boxed{\text{Premrajan}} \]