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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