A thief is noticed by a policeman from a distance of 650 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 8 km and 10.5 km per hour, respectively. The distance (in metres) between them after 12 minutes is:

150

Speed of thief  = 8km/h ×  \(\frac{5}{18}\) =  \(\frac{20}{9}\) m/s

Speed of police = 10.5km/h × \(\frac{5}{18}\) =  \(\frac{17.5}{6}\) m/s

According to the question,

 Distance traveled by thief in 12 mins =  \(\frac{20}{9}\) × (12 × 60) 

=\(\frac{14400}{9}\)= 1600 m

 Distance traveled by police in 12 mins =  \(\frac{17.5}{6}\) × (12 × 60)

=2100 m

 Distance between thief  and police after 12 mins = (Initial distance + distance traveled by a thief in 12 mins) - (Distance traveled by police in 12 mins)

 Distance  = (650 + 1600) - 2100

= 2250 - 2100 = 150 m

SO ,  The distance between them after 12 minutes is 150 m.