The speeds 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 than Kamal to meet each other. If they meet each other at a place P somewhere between L and M, then the distance between P and M is :

Options

A. 220 km
B. 250 km
C. 330 km
D. 320 km

Answer

To solve the problem, we need to determine the distance between point P (where Vimal and Kamal meet) and point M. Here are the steps to find the solution:

### Step 1: Calculate the distance Vimal travels before Kamal starts.
Vimal starts his journey 3 hours earlier than Kamal. Since Vimal's speed is 30 km/h, we can calculate the distance he covers in those 3 hours.

Distance = Speed × Time
Distance = 30 km/h × 3 h = 90 km

### Step 2: Calculate the remaining distance between Kamal and Vimal after 3 hours.
The total distance between L and M is 650 km. After Vimal has traveled 90 km, the remaining distance between them is:

Remaining Distance = Total Distance - Distance covered by Vimal
Remaining Distance = 650 km - 90 km = 560 km

### Step 3: Determine the relative speed of Vimal and Kamal.
Now, we need to find out how fast they are approaching each other. The relative speed is the sum of their speeds since they are moving towards each other.

Relative Speed = Speed of Vimal + Speed of Kamal
Relative Speed = 30 km/h + 40 km/h = 70 km/h

### Step 4: Calculate the time taken for them to meet after Kamal starts.
Now we can calculate the time it takes for them to meet after Kamal starts. We will use the remaining distance and relative speed to find this time.

Time = Remaining Distance / Relative Speed
Time = 560 km / 70 km/h = 8 hours

### Step 5: Calculate the distance Kamal travels until they meet.
Now that we have the time Kamal travels until they meet, we can calculate the distance he covers.

Distance = Speed × Time
Distance = 40 km/h × 8 h = 320 km

### Step 6: Calculate the distance between P and M.
Finally, we find the distance between point P and point M. Since Kamal travels 320 km towards Vimal, the distance from P to M will be:

Distance from P to M = Total Distance - Distance traveled by Kamal
Distance from P to M = 650 km - 320 km = 330 km

Thus, the distance between P and M is **330 km**.

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