3 TIPS on cracking Aptitude Questions on Averages

Looking for Questions instead of tips? - You can directly jump to  Aptitude Test Questions on Averages

Tip #1: If terms are in progression, the average is either the middle term or average of the two middle terms

Question 1: Find the average of first 5 multiples of 3.

Solution:

Number of terms= 5= odd.

Average= Middle term= 3^rd term= 3x3= 9

Question 2: The heights of 6 students in a class are 5ft, 5.2ft, 5.4ft, 5.6ft, 5.8ft and 6ft respectively. What is their average height?

Solution:

Average= Average of middle terms = (5.4+5.6)/2 ft= 5.5ft.

Note: If the terms have a constant difference, the average will be given by:

a.    The middle term if the number of terms is odd.

b.    The average of the two middle or of the two extreme terms. Both will give the same result.

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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?

Solution:

W_{remaining_students} / 59 = (W_{remaining_students} + 45) / 60 + 0.2

60 * W_{remaining_students} = (59 * W_{remaining_students}) + (59 * 45) + (59 *12)

W_{remaining_students} / 59 = 45 + 12 = 57 kgs

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