A thief is spotted by a policeman from a distance of 100 m. 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?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 400 m
The policeman closes the 100 m gap at the difference of the two speeds (relative speed), because both run in the same direction. The thief runs for the whole of that time.
Relative speed \(=10-8=2\) km/hr
Time to close 100 m \(=0.1\) km: \(\displaystyle \frac{0.1}{2}=\frac{1}{20}\) hr
Distance run by the thief in that time \(\displaystyle =8\times\frac{1}{20}=0.4\) km \(=\) 400 m
Shortcut:
The speeds are 8 : 10, so in the same time the thief covers 8 parts while the policeman covers 10; the 2-part difference is the 100 m gap
1 part = 50 m, so the thief runs \(8\times50=400\) m