Quantitative Aptitude

Averages

1,527 Questions
All Basic average and reverse calculation 405 Adding or removing an observation 342 Weighted and combined averages 320 Replacement and correction of a recorded value 233 Ratio shortcut for two-group mixtures 111 Equal-distance average speed 59 Age, score, weight, and spending applications 32 Consecutive terms and arithmetic progressions 25

Averages Questions

Multiple choice

The average mark of a student in 4 subjects is 75. If the student obtained 80 marks in the 5th subject, then the new average is
  1. $77.5$
  2. $77$
  3. $76$
  4. $72.5$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total marks in 4 subjects = 4 × 75 = 300. With 80 marks in 5th subject, new total = 300 + 80 = 380. New average = 380/5 = 76. The average increases because the new score (80) is above the old average (75), pulling the average up. Options A, B, and D result from calculation errors like adding incorrectly or dividing by wrong number of subjects.

Multiple choice

The average of 100 observation was calculated as 35. It was found later, that one of the observations was misread as 83 instead of 53. The correct average is
  1. $32.7$
  2. $34.7$
  3. $35.7$
  4. $36.7$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total of 100 observations = 100 × 35 = 3500. Correct total = 3500 - 83 + 53 = 3470. Correct average = 3470 / 100 = 34.7. The difference of 30 (83 - 53) distributed over 100 observations changes average by 0.3. Option B is correct.

Multiple choice

The average of marks obtained by 100 candidates in a certain examination is 30. If the average marks of passed candidates are 35 and that of the failed candidates is 10, what is the number of the candidates who passed the examination?

  1. 60

  2. 70

  3. 80

  4. 90
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let p be passed candidates. Using the weighted average formula: 35p + 10(100-p) = 30×100. This gives 25p = 2000, so p = 80. Therefore, 80 candidates passed the examination.

Multiple choice

The average of 27 numbers is 60. If one number is changed from 28 to 82, the average is
  1. $56$
  2. $58$
  3. $62$
  4. $64$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The average of 27 numbers is 60, so their sum is 27 × 60 = 1620. When one number changes from 28 to 82, the sum increases by (82 - 28) = 54. The new sum is 1620 + 54 = 1674. The new average is 1674 ÷ 27 = 62. Alternatively, the net change per number is 54/27 = 2, so the average increases by 2: 60 + 2 = 62.

Multiple choice

The average of 11 numbers is 63. If the average of first six numbers is 60 and the average of the last six numbers is 65, then the 6th number is-

  1. 57

  2. 60

  3. 62

  4. 64
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sum of all 11 numbers = 11 × 63 = 693. Sum of first 6 numbers = 6 × 60 = 360. Sum of last 6 numbers = 6 × 65 = 390. The 6th number is counted in both groups, so: (sum of first 6) + (sum of last 6) - (6th number) = sum of all 11. Therefore: 360 + 390 - x = 693, so x = 750 - 693 = 57.

Multiple choice

Average age of 16 persons increased by 4 years if 2 women of 12 years and 18 years are replaced by 2 men. What is the average age of 2 men?

  1. 45

  2. 46

  3. 47

  4. 49
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total age increase for 16 persons = 16 × 4 = 64 years. Two women aged 12 and 18 are replaced, so their combined age = 30 years. Combined age of 2 men = 30 + 64 = 94 years. Average age of 2 men = 94/2 = 47 years. Option B (46) and D (49) are common arithmetic errors from incorrect addition or division.

Multiple choice

The average weight of some students in a class was 58.4 kg. When 5 students having the average weight 62.8 kg joined the class, the average weight of all students in the class increased by 0.55 kg. The number of students initially in the class, were:

  1. 30

  2. 35

  3. 25

  4. 40
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let n be the initial number of students. Total weight = 58.4n. After adding 5 students (total weight = 5 × 62.8 = 314), new average = 58.4 + 0.55 = 58.95. So (58.4n + 314)/(n + 5) = 58.95. Solving: 58.4n + 314 = 58.95n + 294.75, which gives 0.55n = 19.25, therefore n = 35.

Multiple choice

The average age of a number of persons in a group was calculated as 35 years, which was 2.5 years more than the correct average as there was an error in recording the age of two persons as 38.5 years and 40 years instead of 29 years and 22 years respectively. The number of persons in the group was:

  1. 11

  2. 12

  3. 15

  4. 13
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The error in recording caused the average to increase by 2.5 years. The sum of incorrect ages = 38.5 + 40 = 78.5. The sum of correct ages = 29 + 22 = 51. The difference in total sum = 78.5 - 51 = 27.5 years. This error was distributed over n persons, causing the average to increase by 27.5/n = 2.5. Therefore n = 27.5/2.5 = 11.

Multiple choice

A group of three friends, K, L and M, are sitting in a cafe. Their average age is 24 years. Another friend ‘N’ joins the group and the new average age of the group becomes 23 years. If another friend ‘R’, whose age is 2 years more than that of ‘N’, replaces ‘K’, then the average age of L, M, N and R becomes 22.5 years. What is the age of K?

  1. 15 years

  2. 10 years

  3. 12 years

  4. 24 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

K+L+M = 72 (average 24 × 3). When N joins: K+L+M+N = 92 (average 23 × 4), so N = 92-72 = 20. R is 2 years older than N, so R = 22. When R replaces K: L+M+N+R = 90 (average 22.5 × 4). Since L+M+N = 72-K and R = 22, we have (72-K)+22 = 90, so 94-K = 90, giving K = 4. But this doesn't match option D (24). Let me recalculate: K+L+M = 72. K+L+M+N = 92, so N = 20. L+M+N+R = 90 (when R replaces K). But L+M = 72-K, and N = 20, R = 22. So (72-K)+20+22 = 90, which gives 114-K = 90, so K = 24.

Multiple choice

There were 50 students in a hostel. If the number of students increases by 10, the expenses of the mess increase by Rs 180 while the average expenditure per head diminishes by Rs 1. Find the original expenditure of the mess?

  1. 1800

  2. 1600

  3. 1650

  4. 1200
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let original average = x. Original total = 50x. New average = x-1. New total = 60(x-1). But new total = 50x + 180. So 60x - 60 = 50x + 180. Solving: 10x = 240, x = 24. Original expenditure = 50 × 24 = 1200.

Multiple choice

The average age of 30 boys in a class is 10 years. If the age of their teacher is also included, the average age increases by one year. What is the teacher's age?

  1. 38

  2. 30

  3. 40

  4. 41
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total age of 30 boys is 30 × 10 = 300 years. After including the teacher, there are 31 people with an average age of 11 years, so the total becomes 31 × 11 = 341 years. The teacher's age is 341 - 300 = 41 years. This is solved by understanding that the total sum of ages increases when a new person is added.