The speed of a thief is 4/5 times the speed of a policeman. The thief covers a distance of 6 km before he was caught by the policeman in 30 minutes. Initially, what was the distance between the policeman and the thief in km?

Correct option is C

Data:
· Speed of thief = 4/5×"Speed of policeman"
· Distance covered by thief = 6 km
· Time taken = 30 minutes = 1/2 hour
Formulas Used:
· Distance = Speed × Time
Let the speed of the policeman be v km/h.
Solution:
Find the speed of the thief:
"Speed of thief"= $$\frac{4}{5}v$$​​
Distance covered by the thief in 30 minutes:
​$$6=\frac{4}{5 }v×\frac{1}{2} \\\ \\6=\frac{4v}{10}=\frac{2v}{5}$$​​
v = 15 km/h

Find the speed of the thief:
"Speed of thief"= $$\frac{4}{5}×$$​15=12" km/h"
Calculate the distance covered by the policeman in 30 minutes:
"Distance covered by policeman"= $$v×\frac{1}{2}=15×\frac{1}{2}=7.5 \ km$$​​
Initial distance between the policeman and the thief:
"Initial distance"="Distance covered by policeman"-"Distance covered by thief"=7.5-6=1.5" km"
Answer: (c) 1.5