Question : A thief is spotted by a policeman from a distance of 250 m. When the policeman starts the chase, the thief also starts running. Assuming that the speed of the thief is 10 km/h and that of the policeman is 12 km/h, how far would the thief have run before he is caught?
Option 1: 4 km
Option 2: 1.25 km
Option 3: 3 km
Option 4: 2 km
Correct Answer: 1.25 km
Solution :
Distance between the thief and the policeman = 250 m
Speed of the thief = 10 km/h = $\frac{25}{9}$ m/s
Speed of the policeman = 12 km/h = $\frac{10}{3}$ m/s
The relative speed of the thief and the policeman = 12 – 10 = 2 km/h or 2 × $\frac{5}{18}$ = $\frac{5}{9}$ m/s
Time taken by the policeman to catch the thief
T = $\frac{250}{\frac{5}{9}}$
T = 50 × 9 = 450 s
Now the distance travelled by the thief before getting caught
D = $\frac{25}{9}$ × 450
D = 25 × 50 = 1250 m or 1.25 km
∴ The thief ran 1.25 km before he was caught.
Hence, the correct answer is 1.25 km.
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