The document provides examples and explanations for calculating averages from sets of data. It includes 30 practice problems related to averages, with step-by-step explanations for calculating the average, total, or individual values based on given averages of subsets of data. Examples cover topics like finding average age, test scores, salary, weight, and more. Formulae for calculating averages are provided throughout.

1. UNIT - 3
AVERAGES

2. INTRODUCTION:
Average:
Average = (Sum of observations/Number of observations)
Average Speed:
Suppose a man covers a certain distance at X kmph and an equal
distance at Y kmph.
Then, the average speed during the whole journey is {2xy/(x+y)} kmph.

3. 1. The average of first 10 even numbers is?
A. 18 B. 22 C. 11 D. 9

4. EXPLANATION:
Sum of 10 even numbers = 10 * 11 = 110
Average = 110/10 = 11

5. 2. The average of 11 numbers is 10.9. If the average of first six is 10.5
and that of the last six is 11.4 the sixth number is?
A. 11.2 B. 11.3 C. 11.4 D. 11.5

6. EXPLANATION:
1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 119.9 = 11.5
6th number = 11.5

7. 3. The average of first 10 natural numbers is?
A. 5 B. 5.5 C. 5.2 D. 5.6

8. EXPLANATION:
Sum of 10 natural no. = 110/2 = 55
Average = 55/10 = 5.5
FORMULA: N+1 / 2

9. 4. The average of first 10 odd numbers is?
A. 15 B. 12 C. 13 D. 10

10. EXPLANATION:
Sum of 10 odd no. = 100
Average = 100/10 = 10
FORMULA: N

11. 5. The average age of three boys is 15 years and their ages are in
proportion 3:5:7. What is the age in years of the youngest boy?
A. 15 B. 12 C. 13 D. 9

12. 6. The average of 9 observations was 9, that of the 1st of 5 being 10 and
that of the last 5 being 8. What was the 5th observation?
A. 12 B. 11 C. 10 D. 9

13. EXPLANATION:
3x + 5x + 7x = 45
x =3
3x = 9

14. EXPLANATION:
1 to 9 = 9 * 9 = 81
1 to 5 = 5 * 10 = 50
5 to 9 = 5 * 8 = 40
5th = 50 + 40 = 90 – 81 = 9

15. 7. The average of 10 numbers is calculated as 15. It is discovered later
on that while calculating the average, one number namely 36 was
wrongly read as 26. The correct average is?
A. 12 B. 11 C. 10 D. 16

16. EXPLANATION:
10 * 15 + 36 – 26 = 160/10 = 16

17. 8. The average age of 8 men increases by 2 years when two women are
included in place of two men of ages 20 and 24 years. Find the average
age of the women?
A. 24 B. 32 C. 30 D. 36

18. EXPLANATION:
20 + 24 + 8 * 2 = 60/2 = 30

19. 9. A team of eight entered for a shooting competition. The best marks
man scored 85 points. If he had scored 92 points, the average scores for.
The team would have been 84. How many points altogether did the team
score?
A. 625 B. 665 C. 660 D. 675

20. EXPLANATION:
8 * 84 = 672 – 7 = 665

21. 10. The average age of a husband and a wife is 23 years when they were
married five years ago but now the average age of the husband, wife and
child is 20 years(the child was born during the interval). What is the
present age of the child?
A. 4 B. 2 C. 3 D. 6

23. EXPLANATION:
28 * 2 = 56
20 * 3 = 60
-----------
4 years

24. 11. A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150
each and two blankets at a certain rate which is now slipped off from his
memory. But he remembers that the average price of the blankets was
Rs.150. Find the unknown rate of two blankets?
A. 225 B. 265 C. 450 D. 475

25. EXPLANATION:
10 * 150 = 1500
3 * 100 + 5 * 150 = 1050
1500 – 1050 = 450

26. 12. The average temperature for Monday, Tuesday, Wednesday and
Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and
Friday was 46 degrees. If the temperature on Monday was 42 degrees.
Find the temperature on Friday?
A. 34 B. 32 C. 30 D. 36

27. EXPLANATION:
M + Tu + W + Th = 4 * 48 = 192
Tu + W + Th + F = 4 * 46 = 184
M = 42
Tu + W + Th = 192 -42 = 150
F = 184 – 150 = 34

28. 13. Three years ago the average age of a family of six members was 19
years. A boy have been born, the average age of the family is the same
today. What is the age of the boy?
A. 4 B. 2 C. 3 D. 1

29. EXPLANATION:
6 * 22 = 132
7 * 19 = 133
--------------
1

30. 14. The average of five results is 46 and that of the first four is 45. The
fifth result is?
A. 54 B. 52 C. 50 D. 56

31. EXPLANATION:
5 * 46 – 4 * 45 = 50

32. 15. The average of 11 results is 50, if the average of first six results is
49 and that of the last six is 52. Find the sixth result?
A. 54 B. 52 C. 50 D. 56

33. EXPLANATION:
1 to 11 = 11 * 50 = 550
1 to 6 = 6 * 49 = 294
6 to 11 = 6 * 52 = 312
6th = 294 + 312 – 550 = 56

34. 16. Find the average of the first 20 natural numbers?
A. 12.5 B. 11.5 C. 10.5 D. 16.5

35. EXPLANATION:
Average of the first 'n' natural numbers = (n + 1)/2
We get (20 + 1)/2 = 10.5

36. 17. The average of 13 numbers is 60. Average of the first 7 of them is
57 and that of the last 7 is 61. Find the 8th number?
A. 54 B. 61 C. 50 D. 46

37. EXPLANATION:
Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 780 = 46

38. 18. A batsman makes a score of 64 runs in the 16th innings and thus
increased his average by 3. Find his average after the 16th inning?
A. 19 B. 11 C. 15 D. 16

39. EXPLANATION:
Let the average after the 16th inning be P.
So, the average after the 15th inning will be (P-3) Hence, 15(P-30) + 64
= 16P => P = 19

40. 19. The average marks of a class of 30 students is 40 and that of another
class of 50 students is 60. Find the average marks of all the students?
A. 52.5 B. 51.5 C. 50.5 D. 56.5

41. EXPLANATION:
Sum of the marks for the class of 30 students = 30 * 40 = 1200
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 80 students =
1200 + 3000 = 4200
Average marks of all the students = 4200/80 = 52.5

42. 20. The average salary of a person for the months of January, February,
March and April is Rs.8000 and that for the months February, March,
April and May is Rs.8500. If his salary for the month of May is
Rs.6500, find his salary for the month of January?
A. 6250 B. 6500 C. 4500 D. 5000

43. EXPLANATION:
Sum of the salaries of the person for the months of January, February,
March and April = 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March,
April and May = 4 * 8500 = 34000 ----(2)
(2)-(1) i.e. May - Jan = 2000
Salary of May is Rs.6500
Salary of January = Rs.4500

44. 21. The average age of a group of 10 persons was decreased by 3 years
when one person, whose age was 42 years, was replaced by a new
person. Find the age of the new person?
A. 12 B. 11 C. 15 D. 16

45. EXPLANATION:
Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average = (P-3) 10(P-3) = 10P - 42 + Q => Q = 12

46. 22. The average of four positive integers is 69. The highest integer is 93
and the least integer is 39. The difference between the remaining two
integers is 28. Which of the following integers is the higher of the
remaining two integers?
A. 82 B. 81 C. 85 D. 86

47. EXPLANATION:
Let the four integers be A, B, C and D where A > B > C > D.
(A + B + C + D)/4 = 69 => A + B + C + D = 276 ---> (1)
A = 93, D = 39 and B - C = 28
(1) => B + C = 276 - (A + D) = 276 - 132 = 144.
B + B -28 = 144
B = (144 + 28)/2 = 86

48. 23. The average mark of the students of a class in a particular exam is
80. If 5 students whose average mark in that exam is 40 are excluded,
the average mark of the remaining will be 90. Find the number of
students who wrote the exam.
A. 22 B. 21 C. 25 D. 26

49. EXPLANATION:
Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 40) = 90(x - 5)
250 = 10x => x = 25

50. 24. The average height of 50 pupils in a class is 150 cm. Five of them
whose height is 146 cm, leave the class and five others whose average
height is 156 cm, join. The new average height of the pupils of the class
(in cm) is
A. 151 B. 165 C. 150 D. 155

51. EXPLANATION:
Total height = 150 * 50 = 7500 cm.
New average = [7500 - 5 * 146 + 5 * 156 ] / 50 = 151 cm

52. 25. The average age of students of a class is 15.8 years. The average age
of boys in the class is 16.4 years and that of the girls is 15.4 years. The
ration of the number of boys to the number of girls in the class is:
A. 2:3 B. 3:2 C. 1:2 D. 2:1

53. EXPLANATION:
Let the ratio be k : 1. Then,
k * 16.4 + 1 * 15.4 = (k + 1) * 15.8
= (16.4 - 15.8)k = (15.8 - 15.4)
= k = 0.4/0.6 = 2/3
Required ratio = 2/3 : 1 = 2:3

54. 26. The average age of husband, wife and their child 3 years ago was 27
years and that of wife and the child 5 years ago was 20 years. The
present age of the husband is:
A. 42 B. 40 C. 45 D. 46

55. EXPLANATION:
Sum of the present ages of husband, wife and child = (27 * 3 + 3 * 3) =
90 years.
Sum of the present age of wife and child = (20 * 2 + 5 * 2) = 50 years.
Husband's present age = (90 - 50) = 40 years.

56. 27. The mean weight of a class of 35 students is 45 kg. If the weight of
the teacher be included, the mean weight increases by 500 g. Find the
weight of the teacher.
A. 62 B. 60 C. 65 D. 63

57. EXPLANATION:
Mean weight of 35 students = 45 kg.
Total weight of 35 students = (45 × 35) kg = 1575 kg.
Mean weight of 35 students and the teacher (45 + 0.5) kg = 45.5 kg.
Total weight of 35 students and the teacher = (45.5 × 36) kg = 1638 kg.
Weight of the teacher = (1638 - 1575) kg = 63 kg.
Hence, the weight of the teacher is 63 kg.

58. 28. The mean of five numbers is 28. If one of the numbers is excluded,
the mean gets reduced by 2. Find the excluded number.
A. 32 B. 30 C. 35 D. 36

59. EXPLANATION:
Mean of 5 numbers = 28.
Sum of these 5 numbers = (28 x 5) = 140.
Mean of the remaining 4 numbers = (28 - 2) =26.
Sum of these remaining 4 numbers = (26 × 4) = 104.
Excluded number
= (sum of the given 5 numbers) - (sum of the remaining 4 numbers)
= (140 - 104)
= 36.
Hence, the excluded number is 36.

60. 29. A pupil's marks were wrongly entered as 83 instead of 63. Due to
the average marks for the class got increased by half. The number of
pupils in the class is:
A. 42 B. 40 C. 45 D. 46

61. EXPLANATION:
Let there be x pupils in the class.
Total increase in marks = (x * 1/2) = x/2
x/2 = (83 - 63) => x/2 = 20 => x = 40

62. 30. The average weight of A, B and C is 45 kg. If the average weight of
A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
A. 32 B. 30 C. 31 D. 36

63. EXPLANATION:
Let A, B, C represent their respective weights.
Then, we have:
A + B + C = (45 * 3) = 135 --- (i)
A + B = (40 * 2) = 80 --- (ii)
B + C = (43 * 2) = 86 --- (iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 --- (iv)
Subtracting (i) from (iv), we get: B = 31
B's weight = 31 kg.

64. THANK YOU..,

65. In the first 10 overs of a cricket
game, the run rate was only
3.2. What should be the run
rate in the remaining 40 overs
to reach the target of 282 runs?

66. A family consists of two grandparents,
two parents and three grandchildren.
The average age of the grandparents is
67 years, that of the parents is 35 years
and that of the grandchildren is 6 years.
What is the average age of the family?

67. A grocer has a sale of Rs. 6435,
Rs. 6927, Rs. 6855, Rs. 7230 and
Rs. 6562 for 5 consecutive
months. How much sale must he
have in the sixth month so that he
gets an average sale of Rs. 6500?

68. The average weight of 8 person's
increases by 2.5 kg when a new
person comes in place of one of
them weighing 65 kg. What might
be the weight of the new person?

69. The average monthly income of P
and Q is Rs. 5050. The average
monthly income of Q and R is Rs.
6250 and the average monthly
income of P and R is Rs. 5200. The
monthly income of P is: