To find the average of a set of numbers, you add up all the values and then divide the sum by the total number of values in the set.
15 MCQs (Multiple Choice Questions) related to averages, along with their solutions:
Question 1: The average of three numbers is 25.
If two numbers are 30 and 20, what is the third number?
a) 15
b) 25
c) 35
d) 40
Solution: Let the third number be x.
The average of three numbers is (30 + 20 + x) / 3 = 25.
Solving for x, we get x = 25.
Therefore, the third number is option b) 25.
Question 2: The average of five consecutive even numbers is 34.
What is the largest among these numbers?
a) 30
b) 32
c) 36
d) 38
Solution: Let the first even number be x.
The five consecutive even numbers are x, x+2, x+4, x+6, and x+8.
The average is (x + (x+2) + (x+4) + (x+6) + (x+8)) / 5 = 34.
Solving for x, we get x = 32. Therefore, the
largest number is x + 8 = 32 + 8 = 40. Hence,
the correct answer is option d) 38.
Question 3: The average of 7 numbers is 15.
If one of the numbers is 21,
what is the average of the remaining numbers?
a) 13
b) 14
c) 15
d) 16
Solution: Let the sum of the remaining 6 numbers be x.
The average of 7 numbers is (x + 21) / 7 = 15. Solving for x, we get
x = 84. The average of the remaining 6 numbers is
x / 6 = 84 / 6 = 14. Therefore, the correct answer is option b) 14.
Question 4: The average age of 20 students in a class is 12 years.
If the teacher's age is included, the average becomes 13 years.
What is the teacher's age?
a) 30 years
b) 31 years
c) 32 years
d) 33 years
Solution: Let the sum of ages of 20 students be x.
The average age of 20 students is x / 20 = 12. Solving for x, we get x = 240.
When the teacher's age is included, the total sum of ages
becomes (x + T), where T is the teacher's age.
The new average is (x + T) / 21 = 13.
Substituting the value of x, we get (240 + T) / 21 = 13.
Solving for T, we get T = 273 - 240 = 33 years.
Therefore, the teacher's age is option d) 33 years.
Question 5: The average weight of a group of 8 people increases
by 2 kg when a new person of 70 kg joins the group.
What was the average weight of the group before the new person joined?
a) 63 kg
b) 65 kg
c) 67 kg
d) 69 kg
Solution: Let the average weight of the group before the new person
joined be x. The total weight of the 8 people before is 8x.
After the new person joins, the total weight becomes 8x + 70.
The new average is (8x + 70) / 9 = x + 2. Solving for x,
we get x = 66. Therefore, the average weight of the
group before the new person joined is option c) 67 kg.
Question 6: The average of 10 numbers is 20. If each number is
multiplied by 2, what will be the new average?
a) 10
b) 15
c) 20
d) 40
Solution: If each number is multiplied by 2,
the new average will also be multiplied by 2.
Therefore, the new average will be 20 * 2 = 40.
Hence, the correct answer is option d) 40.
Question 7: The average score of a basketball team for the first
8 games is 80 points. If the team scores 95 points in the
9th game, what will be the new average score?
a) 80
b) 82
c) 85
d) 86
Solution: The total score of the first 8 games is 8 * 80 =
640 points. The total score after the 9th game is
640 + 95 =735 points. The new average is 735 / 9 = 82.
Therefore, the correct answer is option b) 82.
Question 8: The average height of a group of 5 people is 160 cm.
If a person of 170 cm height leaves the group,
what will be the new average height?
a) 155 cm
b) 158 cm
c) 160 cm
d) 165 cm
Solution: The total height of the 5 people before is
5 * 160 = 800 cm. After the person leaves, the total height
becomes 800 - 170 = 630 cm. The new average height is 630 / 4 = 157.5 cm. Rounding off to the nearest integer,
the new average height is 158 cm. Hence,
the correct answer is option b) 158 cm.
Question 9: The average of five numbers is 18.
If one number is 10 and another number is 30,
what is the average of the remaining three numbers?
a) 14
b) 15
c) 16
d) 17
Solution: Let the sum of the remaining three numbers be x.
The average of five numbers is (10 + 30 + x) / 5 = 18.
Solving for x, we get x = 40. The average of the
remaining three numbers is x / 3 = 40 / 3 ≈ 13.33.
Rounding off to the nearest integer, the average of the
remaining three numbers is 13. Hence, the correct answer is option a) 14.
Question 10: The average age of a family of four members is 30 years.
What will be the average age if the youngest member,
whose age is 20, is replaced by the grandfather, whose age is 70?
a) 37.5 years
b) 40 years
c) 45 years
d) 47.5 years
Solution: The total age of the four family members before is
4 * 30 = 120 years. After replacing the youngest member
with the grandfather, the new total age becomes
120 - 20 + 70 = 170 years. The new average age is 170 / 4 =
42.5 years. Therefore, the correct answer is option d) 47.5 years.
Question 11: The average of six numbers is 50.
If each number is increased by 10, what will be the new average?
a) 50
b) 60
c) 70
d) 80
Solution: If each number is increased by 10, the new average
will also increase by 10. Therefore, the new average will
be 50 + 10 = 60. Hence, the correct answer is option b) 60.
Question 12: The average marks of 50 students in a class are 75.
If the marks of two students were misread as 48 and 62
instead of 84 and 92, what is the correct average?
a) 73
b) 74
c) 75
d) 76
Solution: The total marks of the 50 students before the correction
is 50 * 75 = 3750. After correcting the marks, the total marks
become 3750 - 48 - 62 + 84 + 92 = 3816. The correct average is
3816 / 50 = 76.32. Rounding off to the nearest integer,
the correct average is 76. Therefore, the correct answer is option d) 76.
Question 13: The average of five numbers is 12.
If the sum of three numbers is 32, what is the
sum of the remaining two numbers?
a) 6
b) 8
c) 10
d) 12
Solution: Let the sum of the remaining two numbers be x.
The average of five numbers is (32 + x) / 5 = 12.
Solving for x, we get x = 60 - 32 = 28.
Therefore, the sum of the remaining two numbers is option b) 28.
Question 14: The average age of a group of friends is 24 years.
If a new person aged 30 joins the group,
what will be the new average age?
a) 24
b) 25
c) 26
d) 27
Solution: The total age of the group of friends before is n * 24,
where n is the number of friends. After the new person joins,
the total age becomes n * 24 + 30. The new average age is
(n * 24 + 30) / (n + 1). Since we do not know the value of n,
we cannot find the exact new average. However, we can see
that the new average will be more than 24 years since
the total age of the group increases by adding a person aged 30.
Therefore, the correct answer is option c) 26.
Question 15: The average of 9 numbers is 50. If the average of
the first five numbers is 40, what is the average of the
last four numbers?
a) 60
b) 65
c) 70
d) 75
Solution: Let the sum of the first five numbers be x.
The average of the first five numbers is x / 5 = 40.
Solving for x, we get x = 200. The total sum of all 9
numbers is 9 * 50 = 450. The sum of the last four numbers is
450 - 200 = 250. The average of the last four numbers is 250 / 4 = 62.5. Rounding off to the nearest integer,
the average of the last four numbers is 63. Therefore,
the correct answer is option a) 60