**Problems on Averages**

1.
Average = Sum of the
observations/Number of Observations. In short form Average is also known as
Mean or Arithmetic Mean

2.
Sum of observations =
Average x Number of Observations

3.
Number of Observations =
Sum of observations / Average

4.
Average of N consecutive
natural or even or odd numbers or multiples of any number (i.e, numbers which
are in Arithmetic Progression A.P) is the middle number. If N is the odd
number.

Example: Average of 23, 25,27,29,31. Here
we have 5 consecutive odd numbers. So the average is middle number 27

If N is the even number, it is the average
of the middle two numbers

Example: Average of 36, 42, 48,54,60,66. These
are 6 consecutive multiples of 6. So the average of these numbers is average of
middle 2 numbers.

5.
Whatever change occurs to each number, the
same change is applicable to the average also.

Example: The average of 13 observations is
28. If 5 is added to each number, then the average is similarly changed. The
new average will be 28+5= 33

6.
If average of m
observations is x and n observations is y, then average of (m+n) observations
is (mx + ny)/m+n

**Aptitude Questions on Averages:**

**Arithmetic Questions with Answers – Averages**

1.
Find the
average of 83,92,112,137,100?

Explanation : Average = Sum of the observations/Number of
Observations

Average = (83+92+112+137+100)/5

= 524/5 =104.8

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2.
Average of
15 quantities is 25 and average of 10 quantities is 35. Find the average of all
the 25 quantities?

**Explanation :**If average of m observations is x and n observations is y, then average of (m+n) observations is (mx + ny)/m+n

Here m=15 x= 25 and n=10 , y=35

Avearge of all the 25
quantities = (15 x 25 + 10 x 35)/ 15+10

=
(375+350)/25 = 725/25= 29

**Averages Solved Examples with Solutions**

3.
The average
expenditure of a worker for first 5 months is Rs 3500 and average expenditure
for last 7 months is Rs 4500 and his savings are Rs 11000. Find his average
monthly income?

**Explanation:**

Income = Expenditure + Savings

Total expenditure for year = 5 x 3500 + 7 x
4500 = 49000

Savings = Rs 11000

Total annual income= Annual Expenditure +
Annual savings = 49000+11000 = 60000

Average monthly income = 60000/12= Rs 5000

**GMAT Mathematics Free study material – Averages and Applications**

4.
An average
mark of a student in 8 subjects is 56. His marks in 7 subjects are 60,48,56,58,52,
71 AND 67. Find the marks in the 8

^{th}subject?**Explanation :**Sum of the marks in 8 subjects = 8 x 56 =448

Sum
of the marks in 7 subjects = 60+48+56+58+52+71+67 = 412

Marks in the 8

^{th}subject = Marks in 8 subjects - marks in 7 subjects
=
448 -412 =36

**Arithmetic Questions with Answers – Problems on Averages**

5.
The total marks
obtained by a student in Arithmetic, Reasoning, English, Mathematics, Computer
science were 315. He got 60 marks in Arithmetic. His average marks in English,
Mathematics and Computer science were 61.5. Find his marks in Reasoning

**Explanation:**Total marks in A +R +E+M+CS = 315

Marks in Arithmetic A= 60

Average marks in E, M and CS = 61.5 => (E+M+CS)
/3 = 61.5 =>E+M+CS=184.5

Marks in English E => (A +R +E+M+CS)- (A + E+M+CS)

= 315 – (60+184.5)=315-244.5 = 70.5

**Aptitude Questions and Answers for Competitive Examinations - Averages**

6.
The average
score of a player in 9 matches is 36.iF in the 10

^{th}match his score is 48.What is his new average score?**Explanation :**Total score for all 10 matches = total score in 9 matches + score in 10

^{th}match = ( 9 x36) +48 = 384

Average score in 10 matches = 384/10 = 38.4

**Aptitude Questions for Campus Placements – Averages**

7.
The average
of 11 numbers is 45. The average of first 5 numbers is 48 and the average of
last 5 numbers is 36. Find the sixth number?

**Explanation :**

Sum of 11 numbers = 11 x 45 =495

Sum
of first 5 numbers = 5 x48= 240

Sum of last 5 numbers = 5 x 36 = 180

6

^{th}number = Sum of 11 numbers – (Sum of first 5 numbers + sum of the last 5 numbers)8
= 495 –(240+180)= 495-420=75

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8.
The average
of 13 observations is 25. The average of first 7 observations is 28 and that of
last 7 observations is 26.What is the value of 7

^{th}observation?**Explanation:**Sum of 13 observations = 13 x 25 = 325

Sum of 1

^{st}7 observations + Sum of last 7 observations
= 7 x 28 + 7 x 26=196+182=378

( It is sum of 14 observations, here 7

^{th}observation repeated while adding observations)
Therefore 7

^{th}observation = Sum of 14 observations – Sum of 13 observations
= 378- 325 =53

**Aptitude Questions and Answers for Competitive Examinations - Averages**

9.
The average runs
of 11 players of a cricket team were 32. If the runs of the captain were excluded,
then average would become 33.Find the score of the captain?

**Explanation:**Sum of the scores of 11 players = 11 x 32 =352

When runs of the captain excluded, sum of the scores of 10 players = 10
x33 = 330

Score of the captain = Score of 11 players
– Score of 10 players

= 352-330 = 22

**Arithmetic Questions with Answers – Problems on Averages**

10. The average of 15 numbers is 36. The average of first 5 numbers
is 38 and average of last 5 numbers is 40. Find the average of middle 5 numbers?

**Explanation:**Sum of middle 5 numbers = Sum of 15 numbers –(sum of first 5 numbers + sum of last 5 numbers)

Sum of middle 5 numbers = (15x36)-(5x38 +
5x40)

=
540-(190+200) =540- 390=150

Average of middle 5 numbers=150/5 = 30.

**IIM-CAT Quantitative Aptitude free study material – Problems on Average**

11. The average age of 20 students is 14 years. If the age of the
teacher is added, the average will be increased by 2 years. What is the age of
the teacher?

**Explanation :**

Including teacher, there are 21 members.

Total age of 20 students + 1 teacher = 21 x 16 =336

Total age of 20 students = 20x 14
=280

Age of the teacher= 336 – 280 =56 years

**IBPS PO Exams Aptitude Questions – Problems on Averages**

12. The average age of 25 students in a class is 15 years. If the ages
of two teachers are added, the average becomes 17. What is the sum of the ages
of two teachers?

**Explanation:**

Sum of the ages of 25 students + 2 teachers
= 27 x 17 = 459.

Sum of the ages of 25 students = 25 x 15 = 375

Therefore sum of the ages of 2 teachers =
459-375 = 84

**GMAT Quantitative Aptitude – Problems on Averages**

13. The average salary of 30 employees in organization is Rs 12500.
If each employee gets a salary hike of Rs 1250, find their new average salary?

**Explanation:**If each element in the group is increased by same number or decreased by same number, the average changes by same number.

As each employee’s salary is increased by Rs 1250,
their new average salary= Rs 12500+ 1250 = Rs 13750

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14. The average of 15 observations is 36. If each observation is
divided by 4, find the average of new observations?

**Explanation:**If each observation is in the data set is multiplied or divided by same value, their average changes similarly.

Given that each observation is divided by 4, hence their new
average = Previous Average /4 = 36/4 =9