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A policeman spots a thief from 200m. The thief starts running as soon as the policeman starts chasing him. If the speed of the policeman is 10 kmph and that of the thief is 8 kmph, how far the thief will have to run before he is overtaken by the policeman?
1. 800 m
2. 600 m
3. 400 m
4. 300 m

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Correct Answer - Option 1 : 800 m

Given:

Distance = 200 m

Speed of the policeman = 10 kmph

Speed of the thief = 8 kmph

Formula Used :

(i) Distance = d × [a / (b - a)]

Calculations:

d = 200 m ,

⇒ a = 8 kmph = 8 × 5/18 = 20/9 m/s

⇒ b = 10 kmph = 10 × 5/18 = 25/9 m/s

According to the formula

Distance = d × [a / (b - a)]

⇒ Distance = 200 × {(20/9) /[(25/9 – 20/9)]}

⇒ Distance = 200 × 20/9 × 9/5

⇒ Distance = 200 × 4

⇒ Distance = 800 m

The thief will have run 800 m before he is overtaken by the policeman.

Alternate Method:

Relative Speed of policeman = (10 - 8) = 2 × 5/18 = 5/9 m/s

⇒ To catch the thief the policeman must gain 200 m.

⇒ Time taken to gain 200 m = 200 × 9/5 = 360 s

⇒ Actual distance covered by policeman in 360 sec = 360 × 25/9 = 1000 m

∴ Distance covered by the thief = 1000 – 200 = 800 m.

The thief will have run 800 m before he is overtaken by the policeman.

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