The speed of Vimal and Kamal are 30 km/h and 40 km/h initially Kamal is at a place L and vimal is at a place M.the distance between L and M is 650 km.Vimal started his journey 3 hours earlier the Kamal to meet each other.if they meet each other at a place P somewhere between L and M , then What is the distance between L and P ?

Options

A. 220 km
B. 320 km
C. 330 km
D. none of these

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the distance covered by Vimal before Kamal starts.
Vimal starts his journey 3 hours earlier than Kamal. His speed is 30 km/h.

**Distance covered by Vimal in 3 hours:**
\[ \text{Distance} = \text{Speed} \times \text{Time} = 30 \, \text{km/h} \times 3 \, \text{h} = 90 \, \text{km} \]

### Step 2: Calculate the remaining distance between L and M after Vimal's initial travel.
The total distance between L and M is 650 km. After Vimal has traveled 90 km, the remaining distance is:

\[ \text{Remaining distance} = 650 \, \text{km} - 90 \, \text{km} = 560 \, \text{km} \]

### Step 3: Determine the relative speed of Vimal and Kamal.
Kamal's speed is 40 km/h and Vimal's speed is 30 km/h. When they are moving towards each other, their relative speed is the sum of their speeds:

\[ \text{Relative speed} = 30 \, \text{km/h} + 40 \, \text{km/h} = 70 \, \text{km/h} \]

### Step 4: Calculate the time taken for them to meet after Kamal starts.
To find the time taken for them to meet after Kamal starts, we use the remaining distance and the relative speed:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{560 \, \text{km}}{70 \, \text{km/h}} = 8 \, \text{hours} \]

### Step 5: Calculate the distance Kamal travels in that time.
Kamal travels for 8 hours at a speed of 40 km/h. The distance he covers is:

\[ \text{Distance} = \text{Speed} \times \text{Time} = 40 \, \text{km/h} \times 8 \, \text{h} = 320 \, \text{km} \]

### Step 6: Conclusion
The distance between point L and point P (where they meet) is 320 km.

### Final Answer
The distance between L and P is **320 km**.

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