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.