Question : A policeman saw a thief from a distance of 450 m. When the policeman started chasing him, the thief also started running. The ratio of speeds of the thief to the policeman is 7 : 8. After running how much distance (in km) can the policeman catch the thief?
Option 1: 3.75
Option 2: 3.4
Option 3: 3.6
Option 4: 3.15
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Correct Answer: 3.6
Solution :
Let the speed of the police and the thief be $8a$ m/sec and $7a$ m/sec.
⇒ Relative speed $= 8a - 7a=a$ m/sec
Now,
Time taken to catch the thief $= \frac{450}{a}$ sec
⇒ Distance travelled by the policeman $= (\frac{450}{a}) × 8a=3600$ m or 3.6 km
Hence, the correct answer is 3.6.
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