Question : A policeman chasing a thief is 0.5 km behind the thief. The speed of the thief is 80% of the speed of the policeman and the policeman catches him in 12 minutes. What is the speed of the thief (in km/hr)?
Option 1: 10
Option 2: 12.5
Option 3: 15
Option 4: 7.5
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Correct Answer: 10
Solution : Distance between the policeman and the thief = 0.5 km Let the policeman's speed be $x$. Thief's speed = $0.8x$ The policeman catches him in 12 minutes = $\frac{12}{60}$ = 0.2 hour Distance covered by the policeman in 12 minutes = 0.5 + distance covered by the thief in 12 minutes $\therefore0.2x = 0.5 + 0.8x\times 0.2$ ⇒ $0.2x = 0.5 + 0.16x$ $\therefore x = 12.5$ $\therefore$ Speed of the thief = 0.8 × 12.5 = 10 km/hr Hence, the correct answer is 10 km/hr.
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