When two bodies approach each other with the different speeds, the distance between them decreases by `120 m` for every `1 min`.The speeds of the bodies are

Options

A. `2 m//s` and `0.5 m//s`
B. `3m//s & 2m//s`
C. `1.75m//s & 0.25 m//s`
D. `2.5m//s & 0.5m//s`

Explanation

To solve the problem, we need to understand the concept of relative velocity when two bodies are moving towards each other. Here's a step-by-step solution:

### Step 1: Understand the Problem
We have two bodies, A and B, moving towards each other. The distance between them decreases by 120 meters every minute.

### Step 2: Convert Time to Seconds
Since the distance is given per minute, we can convert this time into seconds for easier calculations:
- 1 minute = 60 seconds.

### Step 3: Calculate the Relative Velocity
The decrease in distance of 120 meters in 60 seconds indicates the relative velocity of the two bodies combined. The formula for relative velocity when two objects are moving towards each other is:
\[ V_{A} + V_{B} = \frac{\text{Distance Decreased}}{\text{Time}} \]

Substituting the values we have:
\[ V_{A} + V_{B} = \frac{120 \text{ m}}{60 \text{ s}} \]

### Step 4: Perform the Calculation
Now, we can calculate the combined speed:
\[ V_{A} + V_{B} = 2 \text{ m/s} \]

### Step 5: Analyze the Options
We need to find the individual speeds of A and B. However, we only know their sum. The problem does not provide enough information to determine the individual speeds of A and B separately.

### Step 6: Check the Options
We can check the options provided to see which pairs of speeds add up to 2 m/s:
1. 2.5 m/s (not valid)
2. 1.75 m/s and 0.25 m/s (valid, as 1.75 + 0.25 = 2)
3. 3 m/s (not valid)
4. 2.5 m/s and 0.5 m/s (not valid)

### Conclusion
The only valid option that satisfies the condition \( V_{A} + V_{B} = 2 \text{ m/s} \) is:
- **1.75 m/s and 0.25 m/s.**

Thus, the speeds of the bodies are **1.75 m/s** and **0.25 m/s**.

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