Arun and Bhaskar start from place P at 6:00 am and 7:30 am, respectively and run in the same direction. Arun and Bhaskar run at 8 km/h and 12 km/h, respectively. Bhaskar overtakes Arun at

Options

A. `10 :30 am`
B. `9 :10 am`
C. `11 :30 am`
D. `1 :00 am`

Answer

To solve the problem of when Bhaskar overtakes Arun, we can follow these steps:

### Step 1: Determine the time difference between Arun and Bhaskar's start times.
- Arun starts at 6:00 am.
- Bhaskar starts at 7:30 am.
- The time difference is 1.5 hours (or 1 hour and 30 minutes).

**Hint:** Calculate the difference in start times to understand how long Arun has been running before Bhaskar starts.

### Step 2: Calculate the distance Arun covers before Bhaskar starts.
- Arun's speed = 8 km/h.
- Time before Bhaskar starts = 1.5 hours.
- Distance covered by Arun = Speed × Time = 8 km/h × 1.5 hours = 12 km.

**Hint:** Use the formula for distance (Distance = Speed × Time) to find out how far Arun has run before Bhaskar begins.

### Step 3: Determine the relative speed between Bhaskar and Arun.
- Bhaskar's speed = 12 km/h.
- Arun's speed = 8 km/h.
- Relative speed = Bhaskar's speed - Arun's speed = 12 km/h - 8 km/h = 4 km/h.

**Hint:** The relative speed is the difference in their speeds since they are moving in the same direction.

### Step 4: Calculate the time it takes for Bhaskar to catch up to Arun.
- Distance to cover = 12 km (the distance Arun has already covered).
- Time taken by Bhaskar to overtake Arun = Distance / Relative Speed = 12 km / 4 km/h = 3 hours.

**Hint:** Use the formula for time (Time = Distance / Speed) to find out how long it will take Bhaskar to catch up.

### Step 5: Determine the time at which Bhaskar overtakes Arun.
- Bhaskar starts at 7:30 am.
- Time taken to catch up = 3 hours.
- Overtaking time = 7:30 am + 3 hours = 10:30 am.

**Hint:** Add the time taken to catch up to Bhaskar's start time to find the exact time of overtaking.

### Final Answer:
Bhaskar overtakes Arun at **10:30 am**.

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