Average Practice Test for Aptitude Exams -- Free Practice

Question 1

The mean salary for a group of 40 female workers is Rs. 5200 per month and that for a group of 60 male workers is Rs. 6800 per month. What is the combined mean salary?

A

Rs. 6160✓✗

B

Rs. 6280✓✗

C

Rs. 6890✓✗

D

Rs. 6920✓✗

Explanation

Combined mean = (40 × 5200) + (60 × 6800)40 + 60
= 2,08,000 + 4,08,000100 = 6,16,000100 = 6160

Question 2

The mean weight of 15 students is 110 kg. The mean weight of 5 of them is 100 kg and that of another five students is 125 kg, then the mean weight of the remaining students is:

A

120✓✗

B

105✓✗

C

115✓✗

D

None of these✓✗

Explanation

Total weight of 15 students = 15 × 110 = 1650 kg
Weight of first 5 students = 5 × 100 = 500 kg
Weight of next 5 students = 5 × 125 = 625 kg
Weight of remaining 5 students = 1650 - 500 - 625 = 525 kg
Mean of remaining 5 students = 525 / 5 = 105 kg

Question 3

The average age of 15 students is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, then the age of the 15th student is:

A

11 years✓✗

B

14 years✓✗

C

15 years✓✗

D

None of these✓✗

Explanation

Total age of 15 students = 15 × 15 = 225 years
Sum of first 5 students' ages = 5 × 14 = 70 years
Sum of next 9 students' ages = 9 × 16 = 144 years
Sum of these 14 students = 70 + 144 = 214 years
Age of the 15th student = 225 - 214 = 11 years

Question 4

In a group of persons, the average weight is 60 kg. If the average weight of males and females taken separately is 80 kg and 50 kg respectively, find the ratio of the number of males to that of females.

A

2:3✓✗

B

3:2✓✗

C

2:1✓✗

D

1:2✓✗

Explanation

Let the number of males and females be m and f.
80m + 50fm + f = 60
80m + 50f = 60m + 60f
20m = 10f
f = 2m, so m : f = 1 : 2

Question 5

The mean of 100 students was 45. Later on, it was discovered that the marks of two students were misread as 85 and 54 instead of 58 and 45. Find the correct mean.

A

68✓✗

B

36✓✗

C

44.64✓✗

D

52✓✗

Explanation

Total (with wrong values) = 100 × 45 = 4500
Wrong values sum = 85 + 54 = 139. Correct values sum = 58 + 45 = 103
Correct total = 4500 - 139 + 103 = 4464
Correct mean = 4464 / 100 = 44.64

Question 6

The average of marks obtained by 120 students in a certain examination is 35. If the average marks of passed students is 39 and that of the failed students is 15, what is the number of students who passed in the examination?

A

100✓✗

B

150✓✗

C

200✓✗

D

None of these✓✗

Explanation

Let p = number who passed, f = number who failed. p + f = 120.
39p + 15f = 35 × 120 = 4200
39p + 15(120 - p) = 4200
39p + 1800 - 15p = 4200
24p = 2400
p = 100

Question 7

The mean of the first 3 terms is 14 and the mean of the next 2 terms is 18. The mean of the 5 numbers is:

A

14.5✓✗

B

15✓✗

C

14✓✗

D

15.6✓✗

Explanation

Sum of first 3 terms = 3 × 14 = 42
Sum of next 2 terms = 2 × 18 = 36
Total sum = 42 + 36 = 78
Mean of all 5 = 78 / 5 = 15.6

Question 8

The mean of a set of 20 observations is 18.3. The mean is reduced by 0.6 when a new observation is added to the set. The new observation is:

A

17.6✓✗

B

18.0✓✗

C

5.7✓✗

D

24.6✓✗

Explanation

Original total (20 obs) = 20 × 18.3 = 366
New mean (21 obs) = 18.3 - 0.6 = 17.7
New total = 21 × 17.7 = 371.7
New observation = 371.7 - 366 = 5.7

Question 9

The mean salary of a group of 50 persons is Rs. 5850. Later it is discovered that the salary of one person had been wrongly taken as Rs. 8000 instead of Rs. 7800. The corrected mean salary is:

A

Rs. 5854✓✗

B

Rs. 5846✓✗

C

Rs. 5640✓✗

D

None of these✓✗

Explanation

Original total = 50 × 5850 = 2,92,500
Corrected total = 2,92,500 - 8000 + 7800 = 2,92,300
Corrected mean = 2,92,300 / 50 = 5846

Question 10

A company's past 10 years' average earnings is Rs. 40 crores. To have the same average earnings for 11 years including these 10 years, how much earning must be made by the company in the eleventh year?

A

Rs. 40 crores✓✗

B

40 × 1011 crores✓✗

C

More than Rs. 40 crores✓✗

D

None of these✓✗

Explanation

For the average to remain unchanged after adding a new value, that new value must equal the existing average itself.
Since the average of the first 10 years is already Rs. 40 crores, the 11th year must also earn exactly Rs. 40 crores.

Question 11

The average of 15 numbers is 15. If the average of the first five numbers is 14 and that of the last nine numbers is 16, then find the sixth number.

A

12✓✗

B

11✓✗

C

10✓✗

D

9✓✗

Explanation

Total of 15 numbers = 15 × 15 = 225. Total of the other 14 numbers = (14 × 5) + (16 × 9) = 70 + 144 = 214. Sixth number = 225 – 214 = 11.

Question 12

The average of four consecutive even numbers is 27. Find the largest of these numbers.

A

28✓✗

B

30✓✗

C

32✓✗

D

34✓✗

Explanation

Let the numbers be x, (x+2), (x+4), (x+6). 4x + 124 = 27, so x = 24. Largest number = x + 6 = 30.

Question 13

There are two batches A and B of a class. Batch A consists of 36 students and batch B consists of 44 students. Find the average weight of whole class, if average weight of batch A is 40 kg and that of batch B is 35 kg.

A

29.23 kg✓✗

B

32.56 kg✓✗

C

35.66 kg✓✗

D

37.25 kg✓✗

Explanation

Total weight = (36 × 40) + (44 × 35) = 1440 + 1540 = 2980 kg. Total students = 36 + 44 = 80. Average weight = 298080 = 37.25 kg.

Question 14

The average age of a class of 29 students is 20 years. If the age of teacher is included, then the average increases by 3 months. Find the age of the teacher.

A

25.2 years✓✗

B

27.5 years✓✗

C

29 years✓✗

D

31.5 years✓✗

Explanation

Total age of 29 students = 20 × 29 = 580 years. Average age of 29 students + 1 teacher = 20 years + 3 months = 814 years. Total age of 30 people = 814 × 30 = 607.5 years. Age of teacher = 607.5 – 580 = 27.5 years.

Question 15

2 years ago, the average age of a family of 5 members was 16 years. After a baby is born, the average age of family is the same today. Find the present age of the baby.

A

4 years✓✗

B

6 years✓✗

C

8 years✓✗

D

812 years✓✗

Explanation

Total age of 5 members 2 years ago = 16 × 5 = 80 years. Present total age of the 5 members = 80 + (2 × 5) = 90 years. Total age of 6 members today (with the baby) = 16 × 6 = 96 years. Age of baby = 96 – 90 = 6 years.

Question 16

John's marks were wrongly entered as 83 instead of 63. If the average marks calculated for the whole class increased by half a mark, then find the number of students in the class.

A

30✓✗

B

35✓✗

C

40✓✗

D

45✓✗

Explanation

Let the number of students be x. Total increase in marks = x2, which equals the error 83 – 63 = 20. So x2 = 20, giving x = 40.

Question 17

The mean of 40 observations was 46. Later on it was found that an observation 38 was wrongly taken as 33. Find the corrected value of mean.

A

40.23✓✗

B

42.36✓✗

C

46.13✓✗

D

51.23✓✗

Explanation

Sum of observations = 46 × 40 = 1840. Correct sum = 1840 + (38 – 33) = 1845. Corrected mean = 184540 = 46.125 ≈ 46.13.

Question 18

A person covers a distance of 60 km from P to Q at a speed of 20 km/hr and returns from Q to P at a speed of 30 km/hr. Find the average speed of person.

A

22 km/hr✓✗

B

24 km/hr✓✗

C

26 km/hr✓✗

D

28.2 km/hr✓✗

Explanation

For a round trip covering equal distances, Average Speed = 2 V₁ V₂V₁ + V₂. With V₁ = 20 km/hr, V₂ = 30 km/hr: Average Speed = 2 × 20 × 3020 + 30 = 120050 = 24 km/hr.

Question 19

A batsman makes a score of 80 runs in the 16^th inning and increases average by 3. What is his average after 16^th inning?

A

35✓✗

B

32✓✗

C

29✓✗

D

25✓✗

Explanation

Let the average after the 16^th inning be X, so the average after the 15^th inning was (X – 3). 15(X – 3) + 80 = 16X. Solving: 15X – 45 + 80 = 16X, giving X = 35.

Question 20

In a cricket match, 6 players had an average X of their runs. Average increases by 10 runs, if seventh player makes a score of 112 runs. What is the average of first 6 players.

A

36✓✗

B

39✓✗

C

40✓✗

D

42✓✗

Explanation

Sum of first 6 players' scores = 6X. With the 7th player: 6X + 1127 = X + 10. Solving: 6X + 112 = 7X + 70, giving X = 42.

Question 21

The average of 25 numbers is 18. The average of the first 12 numbers is 14, while that of the last 12 is 17. What is the thirteenth number?

A

78✓✗

B

87✓✗

C

92✓✗

D

None of these✓✗

Explanation

Total sum = 25 × 18=450. Sum of first 12 = 12 × 14=168. Sum of last 12 = 12 × 17=204. 13th number = 450-(168+204) = 78.

Question 22

The average of 20 numbers is 0. Of them, at most how many may be greater than zero?

A

0✓✗

B

1✓✗

C

19✓✗

D

Data insufficient✓✗

Explanation

If 19 numbers are positive summing to S, the 20th can be -S, giving average 0. All 20 cannot be positive (average would be positive), so the maximum is 19.

Question 23

After 10 innings, the average runs of a cricket player are 32. How many runs does he need to score in the next inning to increase his average by 4 runs?

A

2✓✗

B

4✓✗

C

36✓✗

D

76✓✗

Explanation

New average = 36 over 11 innings, so new total = 36 × 11=396. Current total = 32 × 10=320. Runs needed = 396-320 = 76.

Question 24

The average of 5 numbers is 27. One number is excluded and the average becomes 25. What is the excluded number?

A

25✓✗

B

27✓✗

C

35✓✗

D

40✓✗

Explanation

Total sum = 5 × 27=135. Sum of remaining 4 = 4 × 25=100. Excluded number = 135-100=35.

Question 25

There are 36 students in a group. The average age of the group is 14 years. If the teacher's age is included, the average age of the group increases by 1 year. What is the age of the teacher?

A

36 years✓✗

B

37 years✓✗

C

51 years✓✗

D

Data insufficient✓✗

Explanation

Original total = 36 × 14=504. New total (37 people, average 15) = 37 × 15=555. Teacher's age = 555-504=51.