Question : At 7: 30 P.M. the owner of a Cycle noticed that a thief was taking away his cycle from his home and was cycling in a particular direction at an estimated speed of 10 km per hour. He informed the police about the theft and the policeman started from the same point, half an hour later than the time of the theft but with a speed of 12 km per hour. At what time will the Policeman catch the thief?
Option 1: 10:45 P.M.
Option 2: 9: 30 P.M.
Option 3: 10:00 P.M.
Option 4: 10:30 P.M.
Correct Answer: 10:30 P.M.
Solution :
Relative speed in same direction = 12 – 10 = 2 km/hr
Distance travelled by the thief with a speed of 10 km/hr in 30 mins = $10\times\frac{30}{60}= 5$ km
Time $=\frac{\text{Distance}}{\text{Speed}}=\frac{5}{2}=2.5$ hours
The policeman started at 8:00 P.M., after 2.5 hours, he caught the thief = 8:00 + 2.5 hours = 10:30 P.M.
Hence, the correct answer is 10:30 P.M.
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