A, B and C walk 1 km in 5 min, 8 min and 10 min, respectively. C starts walking from a point at a certain time, B starts from the same point 1 min later and A starts from the same point 2 min later than C Then, A meetBand C at times

Options

A. 2 min , 3min
B. `4/3` min , 3 min
C. `2 ` min , ` 5/3` min
D. 1 min , 2 min

Answer

To solve the problem, we need to determine when A meets B and C based on their walking speeds and starting times. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the Speeds of A, B, and C
- A walks 1 km in 5 minutes.
- Speed of A = \( \frac{1000 \text{ meters}}{5 \text{ minutes}} = 200 \text{ meters/minute} \)

- B walks 1 km in 8 minutes.
- Speed of B = \( \frac{1000 \text{ meters}}{8 \text{ minutes}} = 125 \text{ meters/minute} \)

- C walks 1 km in 10 minutes.
- Speed of C = \( \frac{1000 \text{ meters}}{10 \text{ minutes}} = 100 \text{ meters/minute} \)

### Step 2: Determine the Distances Covered Before A Starts
- C starts walking first. After 2 minutes, the distance covered by C:
- Distance by C in 2 minutes = Speed of C × Time = \( 100 \text{ meters/minute} \times 2 \text{ minutes} = 200 \text{ meters} \)

- B starts 1 minute later than C. So, when B starts, C has already covered 200 meters.
- In the 1 minute before A starts, B covers:
- Distance by B in 1 minute = Speed of B × Time = \( 125 \text{ meters/minute} \times 1 \text{ minute} = 125 \text{ meters} \)

### Step 3: Calculate the Remaining Distance to Meet
- At the time A starts (2 minutes after C), the distances are:
- C has covered 200 meters, so the remaining distance to cover for C to complete 1 km = \( 1000 - 200 = 800 \text{ meters} \)
- B has covered 125 meters, so the remaining distance for B = \( 1000 - 125 = 875 \text{ meters} \)

### Step 4: Determine When A Meets B
- A starts walking after 2 minutes. The distance A needs to cover to meet B:
- B is at 125 meters and A is at 0 meters.

- The distance between A and B when A starts = \( 125 \text{ meters} \)

- The relative speed of A and B = Speed of A - Speed of B = \( 200 - 125 = 75 \text{ meters/minute} \)

- Time taken for A to meet B:
- Time = Distance / Relative Speed = \( \frac{125 \text{ meters}}{75 \text{ meters/minute}} = \frac{125}{75} = \frac{5}{3} \text{ minutes} \)

### Step 5: Determine When A Meets C
- The distance A needs to cover to meet C:
- C is at 200 meters and A is at 0 meters.

- The distance between A and C when A starts = \( 200 \text{ meters} \)

- The relative speed of A and C = Speed of A - Speed of C = \( 200 - 100 = 100 \text{ meters/minute} \)

- Time taken for A to meet C:
- Time = Distance / Relative Speed = \( \frac{200 \text{ meters}}{100 \text{ meters/minute}} = 2 \text{ minutes} \)

### Final Answer
- A meets B in \( \frac{5}{3} \) minutes and A meets C in 2 minutes.