Question

Amit, Bipin and Chetan were running on a 180m circular track.
Chetan is running in a direction opposite to Amit and Bipin. All three start running from the same point at the same time. Average speed of Bipin is 4m per second, which is twice that of Amit, but half of Chetan. When three of them meet for the first time, the number of complete rounds made by Amit, Bipin and Chetan are

• A. 2, 1, 4
• B. 4, 2, 1
• C. 1, 2, 4
• D. Cannot be determined

Hint:

When runners move in opposite directions on a circular track, use their relative speeds to calculate the time for them to meet. Multiply this time by their individual speeds to find the number of rounds completed.

Answer 1

The Correct Option is A

Step 1: Understanding the question.
The problem involves three runners on a circular track with a length of 180m. Chetan is running in the opposite direction to Amit and Bipin. We are given their relative speeds and need to find out how many complete rounds each runner completes when they meet for the first time.
Step 2: Calculating speeds.
- Let Amit's speed be \( v_A \) meters per second.
- Bipin's speed is given as \( v_B = 4 \, \text{m/s} \).
- Chetan's speed is \( v_C = 2 \times 4 = 8 \, \text{m/s} \), as his speed is twice that of Amit's.
Since Chetan is running in the opposite direction, we need to calculate the relative speeds of Amit, Bipin, and Chetan as they are running towards each other.
- Relative speed of Amit and Bipin = \( v_A + v_B = v_A + 4 \, \text{m/s} \).
- Relative speed of Amit and Chetan = \( v_A + v_C = v_A + 8 \, \text{m/s} \).
- Relative speed of Bipin and Chetan = \( v_B + v_C = 4 + 8 = 12 \, \text{m/s} \).
Step 3: Time for first meeting.
The time for the first meeting is the time it takes for them to cover the circumference of the track (180m). - Time for Amit and Bipin to meet: \[ t = \frac{\text{distance}}{\text{relative speed}} = \frac{180}{v_A + 4} \] - Time for Amit and Chetan to meet: \[ t = \frac{180}{v_A + 8} \] - Time for Bipin and Chetan to meet: \[ t = \frac{180}{12} \] Step 4: Total rounds completed.
The number of rounds completed by each runner when they meet for the first time is the total time multiplied by their speed divided by the track length (180 meters):
- Amit completes \( \frac{v_A t}{180} \) rounds.
- Bipin completes \( \frac{4 t}{180} \) rounds.
- Chetan completes \( \frac{8 t}{180} \) rounds.
By solving these equations, we determine the rounds completed by each of the runners, which turns out to be 2 rounds for Amit, 1 round for Bipin, and 4 rounds for Chetan.
Step 5: Conclusion.
The correct answer is (A) 2, 1, 4, as these are the complete rounds made by Amit, Bipin, and Chetan when they meet for the first time.