The document discusses various concepts and properties related to averages including: 1) What is an average and how it is calculated. 2) Properties of averages such as how the average changes when values are increased, decreased, multiplied, or divided. 3) The range of possible average values based on the highest and lowest numbers. 4) Examples of average problems involving multiple numbers, groups of students, and weighted averages.

1. Bank Exams and SSC
Averages – Concept Session
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2. What is average?
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 =
𝑆𝑢𝑚 𝑜𝑓 𝑎𝑙𝑙 𝑣𝑎𝑙𝑢𝑒𝑠
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠

3. Averages
Properties
1. Average lies between the highest and the lowest values of the given
data.
2. Changes in the values and the corresponding changes in the average.
- When each quantity is increased by K
- When each quantity is decreased by K
- When each quantity is multiplied by K
- When each quantity is divided by K
3. The surplus above the average is always equal to the deficit below
the average.
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4. More observations on Averages
Range of the average
If your marks in 5 subjects are at least 20 and at most 80
- can your average be 85?
- can your average be 15?
If A is the average of n numbers, then
lowest of the numbers≤ A ≤ Greatest of the numbers.
 Note: Equality occurs only when the numbers are equal
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5. Averages - Problems
The average of four consecutive numbers A, B, C and D
respectively is 56.5. What is the product of A and C?
(a) 3363
(b) 3306
(c) 3080
(d) 3192
(e) None of these
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(IBPS Clerk 2011)
Answer: option e

6. Average of five numbers is 61. If the average of first and third
number is 69 and the average of second and fourth number is
69, what is the fifth number ?
(a) 31
(b) 29
(c) 25
(d) 35
(e) None of these
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(SBI Clerk 2012)
Answer: option b
Averages - Problems

7. More observations on Averages
Inclusion and Exclusion
Assume a group of students with an average mark of 70.
- What would happen to the average if someone with a mark of 70 joins the group
- What would happen to the average if someone with a mark of 70 leaves the group
- If a group with an average mark of 65 joins the group
- If a group with an average mark of 80 joins the group
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The average weight of 20 students in a class is 45kg. If the teacher
is included, the average becomes 47kg. What is the weight of the
teacher?
A
v
er
a
g
e
No of people
Averages - Problems

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The average weight of 20 students in a class is 45kg. If one of the
student’s younger sister is included, the average becomes 44kg.
What is the weight of the student’s younger sister?
A
v
e
r
a
g
e
No of people
𝐼𝑛𝑐𝑙𝑢𝑑𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 = 𝐴𝑣𝑔 𝑜𝑙𝑑 ± 𝑁 𝑛𝑒𝑤 (∆ 𝐴𝑣𝑔)
Averages - Problems

10. The average marks obtained by 100 candidates in an
examination are 45 If the average marks of the passed students
are 50 while the average marks of the failed students is 40. Then
find the number of students who passed the examination is
a. 30
b. 40
c. 50
d. 60
e. None of these
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(IBPS CIerk 2015)
Answer: option c
Averages - Problems

11. The average height of 8 students is 152 cm. Two more students
of heights 144 cm and 155 cm join the group. What is the new
average height ?
(a) 151.5cm
(b) 152.5cm
(c) 151 cm
(d) 150.5cm
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(SSC Multitasking 2014)
Answer: option a
Averages - Problems

12. The average marks in English subject of a class of 24 students is
56. If the marks of three students were misread as 44, 45 and 61
of the actual marks 48, 59 and 67 respectively, then what would
be the correct average?
(a) 59
(b) 58
(c) 56.5
(d) 57
(e) None of these
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(IBPS PO/MT 2011)
Answer: option d
Averages - Problems

13. The average weight of 15 oarsmen in a boat is increased by 1.6
kg when one of the crew, who weighs 42 kg is replaced by a
new man. Find the weight of the new man (in kg).
(a) 65
(b) 66
(c) 43
(d) 67
(e) None of these
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(SBI Clerk 2014)
Answer: option b
Averages - Problems

14. The sum of the ages of 4 members of a family 5 years ago was
94 years. Today, when the daughter has been married off and
replaced by a daughter-in-law, the sum of their ages is 92.
Assuming that there has been no other change in the family
structure and all the people are alive, what is the difference in
the age of the daughter and the daughter-in law?
(a) 22 years
(b) 11 years
(c) 25 years
(d) 19 years
(e) 15 years
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(IBPSPO/MT 2012)
Answer: option a
Averages - Problems

15. The average of the 9 consecutive positive integers is 63. The
product of the largest and smallest integers is
(a) 3935
(b) 3953
(c) 3853
(d) 3835
(e) None of these
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(Indian Overseas PO 2013 )
Answer: option b
Averages - Problems

16. Weighted Averages
 When groups are involved.
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Two articles costing Rs. 100 and Rs 50 were sold at a profit of 30%
and 40% respectively. What is the overall profit percentage?
Averages - Problems
Answer: 33.33%

18. Average weight of 19 men is 74 kgs, and the average weight of
38 women is 63 kgs. What is the average weight (rounded off to
the nearest integer) of all the men and the women together ?
(a) 59 kgs.
(b) 65 kgs.
(c) 69 kgs.
(d) 67 kgs.
(e) 71 kgs.
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(SBI Clerk 2012)
Answer: option d
Averages - Problems

19. The average age of boys in the class is twice the number of girls
in the class. The ratio of boys and girls in the class of 50 is 4: 1.
The total of the ages (in years) of the boys in the class is
(a) 2000
(b) 2500
(c) 800
(d) 400
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(SSC CGL 2014)
Answer: option c
Averages - Problems

20. The average weight of 25 students is 16 kg. The average weight
of the first 12 students is 14 kg and of the last 12 students is 17
kg. Find the weight of the thirteenth student.
(a) 29 kg
(b) 22 kg
(c) 27 kg
(d) 24 kg
(e) None of these
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(IBPS SO 2015)
Answer: option b
Averages - Problems

21. Mixtures and Alligations
 When two or more qualities with different quantities are
involved.
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If a milkman mixes 2 liters of Milk A costing Rs.6 pre liter and 1 liter
of Milk B costing Rs. 9 per liter, what is the cost per liter of the
mixture?
What if the quantities
mixed are 10 and 5 liters
from Milk A and Milk B
respectively?
Answer: Rs.7 per litre
Cost/Litre (in Rs. ) Quantity
Milk A 6 2
Milk B 9 1
Mixture ?
Mixtures and Alligations - Problems

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How much sugar costing Rs. 6 per kg must be mixed with
30kg of sugar costing Rs. 9 per kg so that the resultant
mixture costs Rs. 7 per kg?
Cost/Kg
(in Rs. )
Quantity
Sugar A 6 ?
Sugar B 9 30
Mixture 7
Answer: 60 Kg
Mixtures and Alligations - Problems

24. Manish brought 25 kg of rice at Rs. 32 per kg and 15 kg of rice
at Rs. 36 per kg. what profit did he get when he mixed the two
varieties together and sold it at Rs. 40.20 per kg?
(a) 25%
(b) 40%
(c) 30%
(d) 20%
(e) None of these
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(IBPS SO 2013)
Answer: option d
Mixtures and Alligations - Problems

25. The average weight of 25 students is 16 kg. The average weight
of the first 12 students is 14 kg and of the last 12 students is 17
kg. Find the weight of the thirteenth student.
(a) 29 kg
(b) 22 kg
(c) 27 kg
(d) 24 kg
(e) None of these
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(IBPS SO 2015)
Answer: option b
Averages - Problems

26. Replacement /substitution
9 Litres out of 90 litres milk are replaced with an equal quantity of water.
Again 9 litres of the resultant mixture is replaced with an equal quantity of
water, if the process in done three times in total. What is the final
concentration of milk in the solution?
Initial Concentration (IC)
Final concentration (FC)
Replacement volume (RV)
Total Volume (TV)
Number of replacements (n)
FC = IC(1- RV/TV)n
Answer: 72.9%
What if different
volumes are replaced
each time?
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27. Practice Problems
The average age of 60 boys in a class was calculated as 12
years. It was later realized that the actual age of one of the boys
in the class was 12.5 years but it was calculated as 14 years.
What is the actual average age of the boys in the class?
(a) 11 years
(b) 11.275 years
(c) 11.50 years
(d) 11.975 years
(e) None of these
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(SBI Clerk 2014)
Answer: option d

28. Practice Problems
The average age of seven boys sitting in a row facing North is 26
years. If the average age of the first three boys is 19 yrs and the
average age of the last three boys is 32 yrs. What is the age of the boy
who is sitting in middle of the row?
(a) 28 yrs
(b) 29 yrs
(c) 24 yrs
(d) 31 yrs
(e) None of these
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(IBPS Clerk 2015)
Answer: option b

29. Practice Problems
Vikram scored 72 per cent marks in five subjects together, viz;
Hindi, Science, Maths, English and Sanskrit together, where in
the maximum marks of each subject were 100. How many
marks did Vikram score in Science if he scored 80 marks in
Hindi, 70 marks in Sanskrit, 76 marks in Maths and 65 marks in
English?
(a) 72
(b) 69
(c) 59
(d) 71
(e) None of these
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(IBPS Clerk 2011)
Answer: option b

30. Practice Problems
Find the average of first 20 multiple of 7?
(a) 71.5
(b) 73.5
(c) 75.2
(d) 76.6
(e) None of these
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(IBPS Clerk 2015)
Answer: option b