A bus is moving with a speed of 30 km/hr ahead of a car with a speed of 50 km/hr. How many kilometers apart are they if it takes 15 minutes for the car to catch up with the bus ?

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Submitted by examrobotsa on

Q: 78 (IAS/2002)
A bus is moving with a speed of 30 km/hr ahead of a car with a speed of 50 km/hr. How many kilometers apart are they if it takes 15 minutes for the car to catch up with the bus ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,3,9,3,3,5,1

keywords: 

{'km': [0, 0, 2, 1], 'bus': [0, 0, 1, 1], 'many kilometers': [0, 0, 3, 0], 'speed': [0, 1, 2, 0], 'minutes': [0, 0, 1, 1], 'car': [0, 2, 12, 17]}

The question presents a situation where a car is trying to catch up with a bus. The difference in their speeds is the relative speed by which the car approaches the bus, which is 50 km/hr - 30 km/hr = 20 km/hr. If it takes 15 minutes for the car to catch up to the bus at this speed, you can figure out the distance between them using the formula "time = distance/speed." Converting 15 minutes into hours (15/60 = 0.25 hours) and substituting the values into the formula, you get "0.25 hours = distance / 20km/hr", which results in a distance of 5 km.

Option 1 (5 km) is the correct answer because the calculations clearly prove it.

Option 2 (7.5 km), option 3 (12.5 km), and option 4 (15 km) are incorrect because they would require different values for either the relative speed or the time taken, which contradicts the given problem.

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