Question : A thief steals a bike at 12:30 p.m. and drives it at 48 km/hr. But the theft is discovered after half an hour. The bike owner starts to chase him on another bike at 58 km/hr. The thief will be caught at ________.
Option 1: 3:40 p.m.
Option 2: 3:54 p.m.
Option 3: 3:10 p.m.
Option 4: 3:24 p.m.
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Correct Answer: 3:24 p.m.
Solution :
Speed of thief = 48 km/hr
Distance travelled by him in 30 mins = $48\times \frac{30}{60}=24$ km
Owner speed = 58 km/hr
Their relative speed = 58 – 48 = 10 km/hr
Time = $\frac{\text{Distance}}{\text{Speed}}$ = $\frac{24}{10}=2.4\ \text{hours}$ = 2 hours 24 minutes
The owner started after 30 minutes at 1:00 p.m.
The thief gets caught at 1:00 + 2:24 = 3:24 p.m.
Hence, the correct answer is 3:24 p.m.
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