Question : A thief is noticed by a policeman from a distance of 300 m. The thief starts running and the policeman starts chasing him. The thief and policeman run at the rate of 11 km/hr and 13 km/hr, respectively. After running for how many kilometres will the policeman be able to catch the thief?
Option 1: 1.65
Option 2: 1.85
Option 3: 1.75
Option 4: 1.95
Correct Answer: 1.95
Solution :
Distance between police and the thief = 300 m
Speed of thief = 11 km/hr
Speed of police = 13 km/hr
Relative speed in same direction = 13 – 11 = 2 km/hr
= $2\times\frac{5}{18}$ m/s
= $\frac{5}{9}$ m/s
Time = $\frac{\text{Distance}}{\text{Speed}}$
= $\frac{300}{\frac{5}{9}}$
= $\frac{300\times9}{5}$
= 540 seconds
540 seconds = $\frac{540}{60\times60}=\frac{3}{20}$ hours
Distance travelled by police = speed × time
= $13\times\frac{3}{20}$
= $\frac{39}{20}$
= 1.95 km
Hence, the correct answer is 1.95.
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