Tip #2: If a person travels same distances with different speeds, then the average speed is not the arithmetic mean but the harmonic mean

If a person covers a distance d first at x km/hr and then covers the same distance d at y km/hr, then the average speed is:

= Total distance travelled/ Total time taken

= 2d/ (d/x + d/y)

= 2d/ [(yd + xd)/xy]

= 2dxy/[d(x+y)]

= 2xy/ x+y (Harmonic mean of x and y)

Question: A travels 25km at 50 km/hr and then 25km again with 70km/hr. What is A’s average speed during the whole journey?

Solution:

Average speed for the whole journey

= (2x50x70) / (50+70)= 58.3km/hr

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Tip #3: When dealing with problems where average changes by addition/ removal, create an equation of the form: New_total/New Count = Old_Total/Old Count (+/- Change in Average)

Question: The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. What is the weight of the teacher?

Solution:

(24 * 35 + W_{teacher})/ 25 = 35 + 0.4

24 * 35 + W_{teacher }= 35 * 25 + 10

W_{teacher }= 35 + 10 = 45 kgs

Question: When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students?

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Averages

Average: How to calculate Average, Average Formula, Weighted average, Mean Average, Average Questions with Solutions