Question

Three friends P, Q and R go for morning walks around a ground. They start out together from the gate in the same direction, but walk at different speeds. R walks half as fast as P. Q walks 1.5 times faster than R. P takes 1 minute to take one round around the ground. If they all stop when R has finished 4 rounds, which of the options must be true?

• A. Between the start and the end (not counting the start and the end instances), P and R meet each other thrice.
• B. Between start and the end (not counting the start and the end instances), P meets Q only once.
• C. Q will overtake R once near the Tree.
• D. At the end, P, Q and R will reach the gate at the same time.

Answer 1

The Correct Option is A, B, D

Let's determine how many rounds each of the friends completes and check the given conditions:

• P walks at a speed such that he takes 1 minute to complete 1 round. Therefore, P's speed is 1 round per minute.
• R walks half as fast as P, so R's speed is 0.5 rounds per minute.
• Q walks 1.5 times faster than R, so Q's speed is 0.5 × 1.5 = 0.75 rounds per minute.
• If R completes 4 rounds, it takes him 4 / 0.5 = 8 minutes.
• In 8 minutes, P completes 8 rounds (8 minutes × 1 round/minute).
• In 8 minutes, Q completes 6 rounds (8 minutes × 0.75 rounds/minute).

Now, assess the scenarios:

• Between the start and the end (not counting the instances at start and end), P and R meet each other thrice because P completes 8 rounds and R completes 4 rounds, so they meet each time P laps R, which happens at the 2nd, 4th, and 6th rounds of P.
• Between start and the end (not counting the instances at start and end), P meets Q only once. While P completes 8 rounds, Q completes 6 rounds, meaning they meet after P completes his 4th round, when Q completes his 3rd round.
• At the end, P, Q, and R will reach the gate at the same time since they complete a whole number of rounds in 8 minutes.

• Hence, the correct options are:
  • Between the start and the end (not counting the start and the end instances), P and R meet each other thrice.
  • Between start and the end (not counting the start and the end instances), P meets Q only once.
  • At the end, P, Q, and R will reach the gate at the same time.