Kabir started walking at 5 kmph at 6:00 AM to reach office at 6:30 AM. But he stuck due to some reason for 5 minutes. To cover up the remaining distance on time, he took an auto having speed 30 kmph & reached on time. What is distance covered with auto.

Options

A. 0.50 km
B. 0.44 km
C. 0.66 km
D. 0.55 km

Answer

To solve the problem step by step, we will break down the information given and apply the concepts of speed, time, and distance.

### Step 1: Determine the total time Kabir has to reach the office.
Kabir starts walking at 6:00 AM and needs to reach by 6:30 AM.
- Total time = 30 minutes = 0.5 hours.

**Hint:** Calculate the total time available from the start to the destination.

### Step 2: Calculate the distance Kabir would have covered if he walked the entire time.
Kabir walks at a speed of 5 km/h.
- Distance = Speed × Time
- Distance = 5 km/h × 0.5 hours = 2.5 km.

**Hint:** Use the formula for distance to find out how far he would have gone if he had walked the entire time.

### Step 3: Determine the time lost due to the delay.
Kabir got stuck for 5 minutes, which is equivalent to:
- 5 minutes = 5/60 hours = 1/12 hours.

**Hint:** Convert minutes into hours for consistency in calculations.

### Step 4: Calculate the remaining time Kabir has to reach the office after the delay.
- Remaining time = Total time - Time lost
- Remaining time = 0.5 hours - (1/12 hours) = 0.5 - 0.0833 = 0.4167 hours (approximately 5/12 hours).

**Hint:** Subtract the time lost from the total time to find the remaining time.

### Step 5: Calculate the distance Kabir could cover by walking during the remaining time.
- Distance covered while walking = Speed × Remaining time
- Distance covered = 5 km/h × (5/12 hours) = 25/12 km ≈ 2.083 km.

**Hint:** Again, use the distance formula to find out how far he could walk in the remaining time.

### Step 6: Calculate the distance Kabir needs to cover with the auto.
- Distance covered with the auto = Total distance - Distance covered while walking
- Distance covered with the auto = 2.5 km - (25/12 km) = 2.5 km - 2.083 km = 0.417 km.

**Hint:** Subtract the distance he walked from the total distance to find out how much distance he covered with the auto.

### Step 7: Convert the distance covered with the auto into kilometers.
The distance calculated is approximately 0.417 km, which can be rounded to 0.44 km.

**Hint:** Ensure to round off your final answer correctly if needed.

### Final Answer:
The distance covered with the auto is approximately **0.44 km**.