Cars A and B placed D km away start simultaneously and head towards each other at speeds of 50km/hr and 70 km/hr respectively .if both cars meet at a point 125km from where Car A started what is value of D

Options

A. 250
B. 440
C. 300
D. 400

Answer

To solve the problem, we need to determine the distance \( D \) between cars A and B when they start from their respective positions and move towards each other.

### Step-by-Step Solution:

1. **Identify the distances traveled by each car**:
- Car A travels 125 km before meeting Car B.
- Let the distance traveled by Car B be \( x \) km.

2. **Set up the relationship between the distances**:
- Since both cars are moving towards each other, the total distance \( D \) can be expressed as:
\[ D = \text{Distance traveled by Car A} + \text{Distance traveled by Car B} \]
- Therefore, we have:
\[ D = 125 + x \]

3. **Determine the time taken for Car A to travel 125 km**:
- The speed of Car A is 50 km/hr.
- The time taken \( t_A \) by Car A to travel 125 km is given by:
\[ t_A = \frac{\text{Distance}}{\text{Speed}} = \frac{125}{50} = 2.5 \text{ hours} \]

4. **Calculate the distance traveled by Car B in the same time**:
- The speed of Car B is 70 km/hr.
- The distance \( x \) traveled by Car B in the same time \( t_A \) is:
\[ x = \text{Speed} \times \text{Time} = 70 \times 2.5 = 175 \text{ km} \]

5. **Substitute \( x \) back into the equation for \( D \)**:
- Now we can substitute \( x \) into the equation for \( D \):
\[ D = 125 + 175 = 300 \text{ km} \]

### Final Answer:
The value of \( D \) is **300 km**.

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