Question

A thief is spotted by a policeman from a distance of 100m. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8 km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken ?

• A. 100 m
• B. 200 m
• C. 400 m
• D. 500 m

Answer 1

The Correct Option is C

The problem involves relative speeds and distances. To determine how far the thief runs before being overtaken by the policeman, we'll start by understanding their relative speeds. The following steps outline the solution:

Step 1: Convert speeds from km/hr to m/s.
- Thief's speed = 8 km/hr = \(\frac{8 \times 1000}{3600}\) m/s = \( \frac{20}{9} \) m/s.
- Policeman's speed = 10 km/hr = \(\frac{10 \times 1000}{3600}\) m/s = \( \frac{25}{9} \) m/s.

Step 2: Calculate the relative speed.
Relative speed = Policeman's speed - Thief's speed = \( \frac{25}{9} - \frac{20}{9} \) = \( \frac{5}{9} \) m/s.

Step 3: Convert the initial distance from meters to effect using relative speed.
The initial distance is 100 m. The time taken to close this gap with a relative speed of \( \frac{5}{9} \) m/s is calculated by time = \(\frac{\text{Distance}}{\text{Relative Speed}}\) = \(\frac{100}{\frac{5}{9}}\) = 180 seconds.

Step 4: Calculate the distance run by the thief in this time.
Distance = Speed × Time = \( \frac{20}{9} \) m/s × 180 seconds = 400 meters.

Conclusion: Before being overtaken, the thief will have run 400 meters, thus the correct answer is 400 m.