A thief sees a jeep at a distance of 250m coming towards him at 36 km/h. Thief takes 5 second to realize that there is nothing but the police is approaching him by the jeep and start running away from police at 54km/h. But police realize after 10 secs. When the thief starts running away that he is actually a thief and gives chase at 72 km/h. How long after thief saw police did police catchup with him and what is the distance police had to travel to do so ?

Options

A. 50s , 1000m
B. 65s , 1150m
C. 65s,1300m
D. 45s , 1050m

Answer

To solve the problem step by step, let's break down the information provided and calculate the required values.

### Step 1: Convert Speeds from km/h to m/s
1. **Police Speed**:
- Initial speed of police = 36 km/h
- To convert to m/s: \( \text{Speed in m/s} = \text{Speed in km/h} \times \frac{5}{18} \)
- \( 36 \times \frac{5}{18} = 10 \) m/s

2. **Thief Speed**:
- Speed of thief = 54 km/h
- \( 54 \times \frac{5}{18} = 15 \) m/s

3. **Increased Police Speed**:
- Increased speed of police = 72 km/h
- \( 72 \times \frac{5}{18} = 20 \) m/s

### Step 2: Calculate the Time Taken for Each Event
1. **Time Taken by Thief to Start Running**:
- The thief takes 5 seconds to realize the police are approaching.

2. **Time Taken by Police to Realize**:
- The police take 10 seconds to realize that the thief is running away.

### Step 3: Calculate the Distance Covered by Both
1. **Distance Covered by Police in 10 seconds**:
- Distance = Speed × Time
- Distance covered by police in 10 seconds = \( 10 \, \text{m/s} \times 10 \, \text{s} = 100 \, \text{m} \)

2. **Distance Covered by Thief in 5 seconds**:
- Distance covered by thief in 5 seconds = \( 15 \, \text{m/s} \times 5 \, \text{s} = 75 \, \text{m} \)

### Step 4: Calculate the New Distance Between Thief and Police
- Initial distance = 250 m
- After 5 seconds, the distance covered by the thief = 75 m
- Distance covered by police in 10 seconds = 100 m
- New distance = Initial distance - (Distance covered by police + Distance covered by thief)
- New distance = \( 250 - (100 + 75) = 250 - 175 = 75 \, \text{m} \)

### Step 5: Calculate the Relative Speed
- Relative speed of police with respect to the thief = Speed of police - Speed of thief
- Relative speed = \( 20 \, \text{m/s} - 15 \, \text{m/s} = 5 \, \text{m/s} \)

### Step 6: Calculate the Time Taken for Police to Catch Thief
- Time = Distance / Relative Speed
- Time = \( 75 \, \text{m} / 5 \, \text{m/s} = 15 \, \text{s} \)

### Step 7: Calculate Total Time from When Thief Saw Police
- Total time = Time taken by thief to realize + Time taken for police to catch thief
- Total time = \( 5 \, \text{s} + 15 \, \text{s} = 20 \, \text{s} \)

### Step 8: Calculate the Distance Police Travelled to Catch Thief
- Distance = Speed × Time
- Distance travelled by police = \( 20 \, \text{m/s} \times 15 \, \text{s} = 300 \, \text{m} \)

### Final Answer
- The police catch up with the thief **20 seconds** after the thief saw the police, and the distance the police had to travel to do so is **300 meters**.