BANKING

QUANTITATIVE
APTITUDE

BASIC CIRCLE
DAY - 10

AVERAGE

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BASIC FORMULA

EXAMPLE

Find the average of 52, 54, 56 and 58.

EXAMPLE (52+54+56+58)/4=55

(5+10+20+30+40)/5= 105/5=21

TO FIND THE AVERAGE OF SET NUMBERS FORMULAS

The difference between the given numbers Average = (sum of terms)/ (number of

needs to be same. terms)

IF TOTAL NO. OF ELEMENTS IS ODD Sum of terms = average × number of

terms

𝑛(𝑛+1)
Sum of n numbers =
2

𝑛+1
Average of n numbers=
If the total number of elements is odd, 2

then the middle number will be the Sum of n odd numbers = n2

average.
𝑛2
Average of n odd numbers=
𝑛
EXAMPLE
Sum of n even numbers = n (n+1)
Find the average of 26, 28, 30, 32 and 34.
Average of n even numbers = (n(n+1)) /n
(26+28+30+32+34)/5= 150/5 = 30
= n+1

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Average of squares of first n naturals 68 and 70, respectively. Find the mean
numbers = ((n+1) (2n+1))/6 weight of four friends.

Average of cubes of first n natural (a) 66.5 (b) 66.75 (c) 67.75
numbers
(d) 67 (e) 67.5
= [(n (n+1)/2)2]/n
6. 65, 67, 69, 71, 73, 75, 77 are seven
consecutive odd numbers. Find the
average of them.
Practice Problems
(a) 69.5 (b) 68 (c) 71
Find the average of the following set of
numbers: (d) 71.5 (e) 72

1. Find the average of 51, 25, 37, 48, 32. 7. The runs scored by six players in an IPL
cricket match for a team are 22, 36, 56,
(a) 40 (b) 39 (c) 38.6
70, 86, 102. Find the average runs scored
(d) 41 (e) 39.5 by the players.

2. Find the average of 860, 420, 775, (a) 56.25 (b) 74.4 (c) 62
687, 383.
(d) 68 (e) 72
(a) 615 (b) 618 (c) 521
8. The temperatures of a city in 4 days of
(d) 720 (e) 625 a week are 32, 35, 38, 41. What is the

3. The marks of five students in an average temperature in these four days?

examination is 96, 53, 72, 85, 64. What is (a) 37 (b) 36 (c) 38
the average marks of them?
(d) 37.5 (e) 36.5
(a) 72 (b) 64 (c) 70.5
9. Find the average of the consecutive
(d) 63 (e) 74 numbers 17, 18, 19, 20, 21, 22, 23, 24,

4. Find the average of five consecutive 25.

even numbers 14, 16, 18, 20, 22. (a) 20.5 (b) 26 (c) 21

(a) 17.5 (b) 18 (c) 17 (d) 19 (e) 21.5

(d) 19 (e) 18.5

5. The weight of four friends named 10. The heights of six students in a class
Suresh, Riya, Ramu and Ragu are 64, 66, are 142, 143, 144, 145, 146, 147 (in

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centimetres). What is the average height (d) 35 (e) 28

of all the six students?
17. Average age of 25 students is 14
(a) 143 (b) 142 (c) 144.5 years. The average age of first 15
students is 16 years. Find the average age
(d) 144.25 (e) 144
of remaining 10 students.
11. The average of five consecutive
(a) 6 (b) 11 (c) 7.5
numbers is 20. Find the smallest number?
(d) 8.3 (e) 9.7
(a) 21 (b) 18 (c) 20
18. The average of 17 results is 50. The
(d) 22 (e) 18.5
average of first nine results is 70 and that
12. The average of seven consecutive of last nine is 30. What will be the ninth
even numbers is 26. Find the largest result?
number.
(a) 33 (b) 54 (c) 49
(a) 28 (b) 26 (c) 32
(d) 50 (e) 32
(d) 34 (e) 30
19. The average of 25 numbers is 40. If
13. The average of five consecutive odd the three numbers are not considered
number is 39. Find the difference between whose average is 18, what will be the
the largest and the smallest number. average of remaining numbers?

(a) 8 (b) 10 (c) 41 (a) 41 (b) 52 (c) 43

(d) 33 (e) 4 (d) 35 (e) 54

14. Find the average of first 20 natural 20. Average age of 20 boys is 15 years
numbers.(a) 10.5 (b) 11.5 (c) 10 and the average age of 30 girls is 14

(d) 11 (e) 9.5 years. Find the average age of both boys
and girls.
15. Find the average of first 20 odd
numbers. (a) 22.5 (b) 23 (c) 24.5

(a) 10 (b) 12 (c) 245 (d) 14.5 (e) 14.4

(d) 24 (e) 20

16. Find the average of multiples of 7 up 21. The average runs scored by a cricket

to 50.(a) 29 (b) 21 (c) 32 team of 11 players is 35. If the runs

scored by Kohli (a cricketer in that team)

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is discarded, then the average score of the (a) 18 (b) 17 (c) 15

team is 34. Find the runs scored by Kohli.
(d) 19 (e) 20

(a) 39 (b) 40 (c) 55 27. The average age of a group of

teachers is 31 years. Five new teachers
(d) 41 (e) 45
with an average age of 26 years joined in
22. Ronaldo bought five pants at Rs. 390 that school, thereby decreasing average

each, seven shirts at Rs. 200 each and by 1 year. The initial strength of the
school was
five ties at Rs. 214 each. Find the average
price of all these shopping. (a) 25 (b) 20 (c) 24

(a) 320 (b) 520 (c) 260 (d) 30 (e) 22

(d) 250 (e) 275 28. The average weight of 24 women was
increased by 1 kg if two women of 49 kg
23. The average height of 90 students is are replaced by two men. Find the
162 cm. The mean height of boys is 170 average weight of both the men.

cm and that of girls is 152 cm. Find the (a) 59 (b) 60 (c) 58
number of boys.
(d) 61 (e) 62
(a) 32 (b) 50 (c) 45
29. The average weight of 15 students
(d) 40 (e) 48 decreases by 1 kg if a teacher is included
in place of a 55 kg student. Calculate the
24. Find the average of squares of first weight of that teacher.
seven natural numbers.
(a) 40 (b) 30 (c) 35
(a) 24 (b) 32 (c) 20
(d) 25 (e) 45

(d) 26 (e) 30 30. The average weight of a class of 25

boys and 35 girls is 40 kg. If the average
25. Find the average of cubes of first four
weight of boys is 47 kg. What is the
natural numbers.
average weight of girls?
(a) 28 (b) 25 (c) 23
(a) 30 (b) 37 (c) 35

(d) 21 (e) 24 (d) 40 (e) 38

26. The average of 20 observations is 39. Answer Key

The average decreases by 1 when a new
observation is included. What was the 1. (c) 2. (e) 3. (e) 4. (b) 5. (d) 6. (c) 7.

21st observation? (c) 8. (e) 9. (c) 10. (c) 11. (b) 12. (c) 13.

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(a) 14. (a) 15. (e) 16. (e) 17. (b) 18. (d) (a) 52 (b) 51 (c) 40
19. (c) 20. (e) 21. (e) 22. (c) 23. (b) 24.
(d) 56 (e) 46
(c) 25. (b) 26. (a) 27. (b) 28. (d) 29. (a)
30. (c) 5. The average weight of 10 strawberries
increased by 12 g if one of them weighing
80 g is replaced by another. The weight of
Homework the new strawberry is

1. The average weight of 40 chocolates is (a) 180 g (b) 300 g (c) 260 g
4 g. If the weight of the chocolate box is
(d) 200 g (e) 400 g
included, the average weight increases by
0.2 g. What is the weight of the box? 6. Dhoni has a certain average for 12
innings. In the 13th innings, he scores 100
(a) 12.2 g (b) 8.2 g (c) 6.2 g
runs, thereby increasing his average by 2
(d) 10.2 g (e) 11.5 g runs. His new average is

2. Out of four numbers, the average of (a) 76 runs (b) 74 runs

first three is 20 and that of the last three
(c) 78 runs (d) 72 runs
is 18. If the last number is 25, then the
first number is (e) 68 runs

(a) 21 (b) 31 (c) 23 7. The average age of a group of eight

persons is 20 years and 6 months. Two
(d) 25 (e) 33
persons each 28 years old left the group.
3. The mean of 80 observations was noted The average age of the remaining persons
as 50. It was found later that one of the is
observations was misread as 80 instead of
(a) 26 years (b) 18 years
50. The correct mean is
(c) 22 years (d) 20 years
(a) 46.9 (b) 49.625 (c) 47.3
(e) 28 years
(d) 50.7 (e) 48.225

8. Ten persons went to a 3D cinema hall.

4. In IBPS PO examination, a batch of 55
Nine of them spent Rs. 100 each for the
candidates made an average score of 60 ticket of class I and 10th spent Rs. 90
and another batch of 45 made it only 40. more than the average expenditure of all
What is the overall average score?

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the 10 persons. What was the total money from another. What is the average price
spent by them? he paid per toy?

(a) Rs. 900 (b) Rs. 1100 (c) Rs. 990 (a) Rs. 26 (b) Rs. 25

(d) Rs. 1000 (e) Rs. 1150

(c) Rs. 24 (d) Rs. 28

9. The average age of 50 children of a

(e) None of these
class is equal to 12 years. When the age
of the class teacher is included, the 14. The total marks obtained by a student
average becomes 13 years. Find the age in IBPS CLERK preliminary exam’s English,
of the class teacher. Aptitude and Logical sections together is

(a) 56 (b) 63 (c) 61 60 more than the marks obtained in

Aptitude. What is the average mark
(d) 65 (e) 60
obtained in English and Logical together?
10. What is the average of 15, 25, 35, 45
(a) 32 (b) 38 (c) 30
and 0?

(a) 24 (b) 23 (c) 22 (d) Cannot be determined

(d) 25 (e) 26 (e) None of these

11. Average income of Akshay, Babu and 15. The average weight of seven persons
Cindrella is Rs. 400 but the average is decreased by 4 kg, when one person
income of Akshay and Cindrella is Rs. 300. whose weight is 70 kg is replaced by a
Then what is the income of Babu?
new man. The weight of the new person is

(a) 600 (b) 620 (c) 650

(a) 40 kg (b) 45 kg (c) 47 kg
(d) 500 (e) None of the above
(d) 42 kg (e) None of these
12. Average weight of a class of 40
16. Raina has a mean score of 82 runs in
children is 25 kg. If, however, the weight
of a teacher is included, the average is 10 innings. Find out how many runs are to

increased by 1 kg. What is the weight of be scored in the 11th innings to raise the

the teacher? mean score to 90?

(a) 71 kg (b) 65 kg (c) 61 kg (a) 180 (b) 190 (c) 162

(d) 66 kg (e) None of these (d) 170 (e) 200

13. Berlin bought 20 toys for Rs. 25 each 17. In the first 10 overs of a cricket
from one shop and 30 toys for Rs. 900 match, the run rate was only 4 per over.
What should be the run rate in the

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remaining 40 overs to reach the target of 1. (a) 2. (b) 3. (b) 4. (b) 5. (d) 6. (a) 7.
348 runs? (b) 8. (b) 9. (b) 10. (a) 11. (a) 12. (d) 13.
(d) 14. (c) 15. (d) 16. (d) 17. (a) 18. (c)
(a) 7.70 (b) 6.5 (c) 6.75
19. (c) 20. (a)
(d) 7 (e) 7.5

18. The average weight of 12 dogs is

increased by 1.5 kg when a new dog
comes in place of one of them weighing
22 kg. What might be the weight of the
new dog?

(a) 80 kg (b) 35 kg

(c) 40 kg (d) Data inadequate

(e) None of these

19. The average weight of 10 bags is

increased by 2.8 kg when one bag of 35
kg is replaced by a new bag. Then the
weight of the new bag is

(a) 50 (b) 55 (c) 63

(d) 65 (e) None of these

20. The average runs of three cricketers is

60 runs. If their runs are in the ratio 3 : 5
: 7, then what is the lowest run among
these three cricketers:

(a) 36 runs (b) 60 runs

(c) 84 runs (d) 12 runs

(e) None of these

Answer Key

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