# Averages

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

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

## Learning Pundits Content Team

Written on Sep 28, 2017 8:14:24 PM

__3 TIPS on cracking Aptitude Questions on Averages__

__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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# Averages

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

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