Average - Aptitude MCQ Questions and Solutions with Explanations

21

The average age of 7 members of a family is 40 years. In the family, there are three men, three women and one boy. If the average age of three men is 48 years and average age of three women is 44 years, then the age of the boy is:

A) 6 years B) 2 years C) 4 years D) 8 years

Discuss

Answer & Solution

Answer: Option C

Solution:

According to the question,
Let the age of boy be x
7 × 40 = 3 × 48 + 3 × 44 + 1 × x
280 = 144 + 132 + x
x = 4
Therefore, age of the boy is = 4 years

22

The average of marks obtained by A and B is 15 less than that of average marks obtained by B and C. If the marks obtained by C is 65, What is the marks obtained by A?

A) 35 B) 50 C) 65 D) 80

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{According to the question,}} \cr & \left( {\frac{{B + C}}{2}} \right) - \left( {\frac{{A + B}}{2}} \right) = 15 \cr & \Rightarrow \frac{{B + C - A - B}}{2} = 15 \cr & \Rightarrow \frac{{C - A}}{2} = 15 \cr & \Rightarrow C - A = 30 \cr & C = 65 \cr & \therefore A = 35 \cr} $$

23

The numbers of students in section A and section B of a class are 50 and 62, respectively. The average score in mathematics of all students is 75. If the average score of students in section A is 20% more than that of students in section B, then what is the average score of students in section A (correct to one decimal place)?

A) 85.7 B) 87.5 C) 82.6 D) 84.3

Discuss

Answer & Solution

Answer: Option C

Solution:

20% = $$\frac{1}{5}$$
Let, average marks of section B = 5x
Average marks of section A = 6x
Total marks = 50 × 6x + 62 × 5x = (50 + 62)
300x + 310x = 112 × 75
610x = 8400
x = $$\frac{{840}}{{61}}$$
Average marks of section A students = 6x
= 6 × $$\frac{{840}}{{61}}$$
= 82.6

24

A cricketer whose bowling average is 12.4 runs per wicket, takes 5 wickets for 26 runs in the next innings and thereby decreases his average by 0.4. The number of wickets taken by him till the last match was

A) 64 B) 72 C) 90 D) 85

Discuss

Answer & Solution

Answer: Option C

Solution:

According to the question,
Average mcq question image

The number of wickets taken by him till the last match was = 85 + 5 = 90

25

In a class of 60 students, 40% are girls. The average weight of the boys is 62 kg and that of the girls is 55 kg. What is the average weight of the whole class?

A) 59.2 kg B) 58.5 kg C) 59 kg D) 58.6 kg

Discuss

Answer & Solution

Answer: Option A

Solution:

Total weight = 36 × 62 + 24 × 55 = 2232 + 1320 = 3552
Average = $$\frac{{3552}}{{60}}$$ = 59.2 kg

26

The average of 25 numbers is 64. The average of the first 13 numbers and that of the last 13 numbers are 62.8 and 72.2, respectively. If the 12^th number is 61, and if the 12^th and 13^th numbers are excluded, then what is the average of the remaining number (correct to one decimal place)?

A) 59.2 B) 61.5 C) 60.2 D) 62.2

Discuss

Answer & Solution

Answer: Option C

Solution:

Average of 25 numbers = 64
Sum of 25 numbers = 64 × 25 = 1600
Average of first 13 numbers = 62.8
Sum of first 13 numbers = 62.8 × 13 = 816.4
Average of last 13 numbers = 72.2
Sum of last 13 numbers = 72.2 × 13 = 938.6
13^th number = 816.4 + 938.4 - 1600
= 1754.8 - 1600
= 154.8
12^th number = 61
If we remove 12^th and 13^th number then, sum of remaining numbers = 1600 - 61 - 154.8 = 1384.2
Average $$ = \frac{{1384.2}}{{23}} = 60.18 \sim 60.2$$

27

Average of 7 consecutive odd numbers is 31. If the previous and next odd number to these 7 odd numbers are also included, then what will be the new average?

A) 33 B) 31 C) 35 D) 29

Discuss

Answer & Solution

Answer: Option B

Solution:

∵ Average of 7 consecutive odd numbers = 31
∴ Mid odd number = fourth term = 31
So, seven consecutive number
\[ = \begin{array}{*{20}{c}} {25}&{27}&{29}&{31}&{33}&{35}&{37} \\ \leftarrow & \leftarrow & \leftarrow &{}& \to & \to & \to \\ { - 2}&{ - 2}&{ - 2}&{}&{ + 2}&{ + 2}&{ + 2} \end{array}\]
According to the question,
Previous number will be = 25 - 2 = 23
And next odd number will be = 37 + 2 = 39
Average $$ = \frac{{23 + 39}}{2} = \frac{{62}}{2} = 31$$
∴ Average will remain same because 2 subtracted in previous and 2 added in the next number.

28

There is a number consisting of two digits, the digit in the unit's place is twice than digit in the ten's place and if 2 subtracted from the sum of the digits, the difference is equal to $${\frac{1}{6}^{{\text{th}}}}$$ of the number. The number is-

A) 23 B) 25 C) 26 D) 24

Discuss

Answer & Solution

Answer: Option D

Solution:

Shortcut method:
Do by option
Let the number be 24
Sum of digits = 2 + 4 = 6
⇒ 6 - 2 = $$\frac{1}{6}$$ × 24 = 4 = 4 matched
So, 24 is answer

29

The average age of a cricket team of 11 player is 27 year. If two more players are included in the team the average become 26 years. Then the average age (in year) of the two included player is:

A) 14.5 B) 20.5 C) 26 D) 27

Discuss

Answer & Solution

Answer: Option B

Solution:

Sum of the age of 11 player = 27 × 11 = 297
Sum of age of 11 player + 2 more included player = 13 × 26 = 338
∴ Average of the included player $$ = \frac{{338 - 297}}{2} = \frac{{41}}{2} = 20.5$$

30

There is a group of 8 teachers. One teacher leaves the group and a new teacher joins the group. Due to this the average age of teachers becomes same as the average 2 years ago. If the member who left was aged 42 then what is the age (in years) of new teacher?

A) 22 B) 28 C) 24 D) 26

Discuss

Answer & Solution

Answer: Option D

Solution:

Old teacher age = 42
When one old teacher left the group and joins a new teacher, then average age of group become less 2 years.
∴ New teacher's age =
\[\begin{array}{l} \begin{array}{*{20}{c}} {42 - 8 \times 2}\\ {\,\, \downarrow }\\ {{\rm{total \,number \,of \,teachers}}} \end{array}\\ = 42 - 16\\ = 26{\rm{ \,years}} \end{array}\]