Question

Two runners, Ajay and Vijay complete a 600 m race in 38 seconds and 48 seconds respectively. By how many meters will Ajay defeat Vijay?

• A. 120 m
• B. 140 m
• C. 125 m
• D. 50 m

Hint:

In "defeat by distance" race problems, the key is to freeze the moment the winner crosses the finish line and calculate the position of the other runner at that exact time. The difference in their positions is the answer.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
"Ajay defeats Vijay by X meters" means that when Ajay (the winner) finishes the race, Vijay is X meters behind the finish line. To find this distance, we need to calculate how far Vijay has traveled in the time it took Ajay to complete the race.
Step 2: Key Formula or Approach:
1. Calculate the speed of the slower runner (Vijay). \[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] 2. Calculate the distance covered by Vijay in the time taken by the faster runner (Ajay). \[ \text{Distance} = \text{Speed} \times \text{Time} \] 3. Find the difference between the total race distance and the distance covered by Vijay. \[ \text{Defeat Margin} = \text{Total Distance} - \text{Distance covered by loser} \] Step 3: Detailed Explanation:
Given information:
Race distance = 600 m.
Time taken by Ajay = 38 seconds.
Time taken by Vijay = 48 seconds.
First, let's calculate Vijay's speed: \[ \text{Speed}_{\text{Vijay}} = \frac{\text{Total Distance}}{\text{Time}_{\text{Vijay}}} = \frac{600 \text{ m}}{48 \text{ s}} \] \[ \text{Speed}_{\text{Vijay}} = 12.5 \text{ m/s} \] Now, we need to find out where Vijay is when Ajay crosses the finish line. This happens at t = 38 seconds. Let's calculate the distance Vijay covers in 38 seconds: \[ \text{Distance}_{\text{Vijay in 38s}} = \text{Speed}_{\text{Vijay}} \times \text{Time}_{\text{Ajay}} \] \[ \text{Distance}_{\text{Vijay in 38s}} = 12.5 \text{ m/s} \times 38 \text{ s} \] \[ \text{Distance}_{\text{Vijay in 38s}} = 475 \text{ m} \] This means when Ajay is at the 600 m mark (finish line), Vijay is at the 475 m mark.
The distance by which Ajay defeats Vijay is the difference: \[ \text{Defeat Margin} = 600 \text{ m} - 475 \text{ m} = 125 \text{ m} \] Step 4: Final Answer:
Ajay will defeat Vijay by 125 meters.