A thief steals a car at 1.30 pm. and drives it off at 40 km/hr. The theft is discovered at 2 pm. and the owner sets off in another car at 50 km/hr. He will overtake the thief at.
एक चोर दोपहर 1 : 30 बजे एक कार चुराता है और उसे 40 किमी/घंटा की गति से चलाकर ले जाता है। चोरी का पता दोपहर 2 बजे चल जाता है और कार मालिक एक दुसरी कार में 50 किमी/घंटा की गति पर चलाकर जाता है। वह चोर को कितने बजे पकड़ लेगा?

Options

A. सायं 5 बजे
B. सायं 4 बजे
C. सायं 4:30 बजे
D. सायं 6 बजे

Explanation

To solve the problem step by step, we need to calculate the time it takes for the owner to catch up with the thief after the theft is discovered.

### Step-by-Step Solution:

1. **Determine the time difference when the theft is discovered:**
- The thief steals the car at 1:30 PM.
- The theft is discovered at 2:00 PM.
- Time difference = 2:00 PM - 1:30 PM = 30 minutes = 0.5 hours.

2. **Calculate the distance the thief has traveled by the time the owner starts:**
- Speed of the thief = 40 km/hr.
- Distance traveled by the thief in 0.5 hours = Speed × Time = 40 km/hr × 0.5 hr = 20 km.

3. **Determine the speeds of both the thief and the owner:**
- Speed of the thief = 40 km/hr.
- Speed of the owner = 50 km/hr.

4. **Calculate the relative speed between the owner and the thief:**
- Relative speed = Speed of the owner - Speed of the thief = 50 km/hr - 40 km/hr = 10 km/hr.

5. **Calculate the time it takes for the owner to catch up with the thief:**
- The owner needs to cover the distance of 20 km that the thief has already traveled.
- Time = Distance / Relative Speed = 20 km / 10 km/hr = 2 hours.

6. **Determine the time at which the owner catches the thief:**
- The owner starts chasing the thief at 2:00 PM.
- Time taken to catch the thief = 2 hours.
- Therefore, the owner will catch the thief at 2:00 PM + 2 hours = 4:00 PM.

### Final Answer:
The owner will overtake the thief at **4:00 PM**.