A person travelled from one place to another at an average speed of 40 kilometres/hour and back to the original place at an average speed of 50 kilometres/hour. What is his average speed in kilometres/hour during the entire round-trip ?

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Submitted by examrobotsa on

Q: 136 (IAS/1995)
A person travelled from one place to another at an average speed of 40 kilometres/hour and back to the original place at an average speed of 50 kilometres/hour. What is his average speed in kilometres/hour during the entire round-trip ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,20,20,11,2,20,7

keywords: 

{'average speed': [0, 2, 4, 2], 'kilometres': [0, 1, 0, 1], 'distance': [0, 3, 3, 3], 'hour': [5, 5, 11, 12], 'trip': [0, 1, 0, 1]}

The average speed on a round trip is determined not by the arithmetic mean (adding the two speeds and dividing by 2) but rather by the harmonic mean. This is because the total distance travelled is constant, but the time taken for either leg of the trip depends on the speed.

Option 1 is incorrect because 45 km/hr is the arithmetic mean of 40 and 50, not the harmonic mean.

Option 2 is incorrect because 20 km/hr is much lower than either leg of the journey, and thus could not represent the average speed.

Option 3 is correct because it represents the harmonic mean of 40 and 50. The harmonic mean is calculated by dividing the number of values (2 in this case) by the sum of their reciprocals (1/40 + 1/50). This results in (2/(1/40 + 1/50)) = 400/9 km/hr approximately 44.44 km/hr.

Option 4 is incorrect because the average speed can be calculated regardless of the exact distance, so precise distances are not needed.