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

A shopkeeper bought a total of 20 bags of grains having an average weight of 60.5 kg per bag. Out of these, the average weight of the 7 rice bags was 60 kg per bag, while the average weight of a wheat bag was 4 kg more than that of a maize bag. If 9 of the bags contained wheat while the remaining contained maize, what is the average weight of a maize bag?

  1. 52 kg

  2. 51 kg

  3. 54 kg

  4. 58 kg
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total weight of 20 bags = 20 × 60.5 = 1210 kg. Weight of 7 rice bags = 7 × 60 = 420 kg. Remaining 13 bags are wheat and maize. 9 wheat bags, so 4 maize bags. Let maize bag weight = m kg. Then wheat bag weight = m + 4 kg. Total: 420 + 9(m + 4) + 4m = 1210. Solving: 420 + 9m + 36 + 4m = 1210, so 13m + 456 = 1210, 13m = 754, m = 58 kg. Average weight of maize bag = 58 kg.

Multiple choice

The average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14th number is excluded, then what is the average of remaining numbers? (correct to one decimal places)

  1. 74.7

  2. 75.7

  3. 78.7

  4. 70.7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total sum = 28 × 77 = 2156. Sum of first 14 = 14 × 74 = 1036. Sum of last 15 = 15 × 84 = 1260. Note: The 14th number is counted in both sums. So 1036 + 1260 = 2156 + 14th number. Therefore, 14th number = 2296 - 2156 = 140. New total = 2156 - 140 = 2016. New average = 2016 ÷ 27 = 74.67 ≈ 74.7.

Multiple choice

The average weight of 30 persons of group A is 3 kg more than the average weight of 25 persons of group B. The average weight of 25 persons of group B is 2.5 kg more than the average weight of 20 persons of group C. If the total weight of 30 persons of group A is 1725 kg, then what will be the average weight of the persons of group A and group C taken together (in kg)?

  1. 55.3

  2. 55.4

  3. 55.1

  4. 55
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let a, b, c be average weights of groups A, B, C. Given: a = b + 3, b = c + 2.5, and 30a = 1725. So a = 57.5 kg, b = 54.5 kg, c = 52 kg. Total weight of A = 1725 kg. Total weight of C = 20 × 52 = 1040 kg. Combined average = (1725 + 1040)/(30 + 20) = 2765/50 = 55.3 kg. Option A matches.

Multiple choice

The average score in Mathematics of 90 students of sections A and B of class IX was 63. The number of students in A were 10 more than those in B. The average score of students in A was 30% more than that of students in B. The average score of students in B is:

  1. 52

  2. 54

  3. 59

  4. 56
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let students in section B = x, then section A = x + 10. Total: x + x + 10 = 90, so 2x = 80, x = 40. Section B has 40 students, section A has 50 students. Let average of B = a, then average of A = 1.3a (30% more). Weighted average: (50 × 1.3a + 40 × a) / 90 = 63. So (65a + 40a) / 90 = 63, 105a = 5670, a = 54. Section B's average is 54. This is a standard weighted average problem.

Multiple choice

The average weight of 10 men in a boat is increased by 1 kg when one of the crew who weighs 50 kg is replaced by a new man. What is the weight of the new man?

  1. 58 kg

  2. 52 kg

  3. 53 kg

  4. 60 kg
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When the average of 10 men increases by 1 kg, the total weight increases by 10 x 1 = 10 kg. The new man weighs 10 kg more than the man he replaced (50 kg), so his weight is 60 kg. Option A (58 kg) would only increase the average by 0.8 kg, not the full 1 kg stated.

Multiple choice

The average height of some students in a group is 156 cm. If 5 students of average height 160 cm join the group, then the average height of all the students in the group increases by 0.8 cm. What is the number of students in the group, initially?

  1. 20

  2. 15

  3. 25

  4. 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let initial students = n, average = 156. Total height = 156n. 5 new students with average 160 cm join, so their total = 5 × 160 = 800. New average = 156 + 0.8 = 156.8, new total = (n + 5) × 156.8. Equation: 156n + 800 = 156.8(n + 5). Solving: 156n + 800 = 156.8n + 784. So 800 - 784 = 156.8n - 156.8, giving 16 = 0.8n, thus n = 20. Initially there were 20 students.

Multiple choice

The average score of 40 students in a class test is 45. Later on, it was found that at two places 25 was read as 35 and at one place 38 was read as 32. What is the actual average score of the class?
  1. $44.65$
  2. $45.35$
  3. $39.69$
  4. $43.80$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Two errors: 25 read as 35 (excess +10) twice adds +20 to total. 38 read as 32 (deficit -6) once adds -6 to total. Net excess = +20 - 6 = +14. Correct total = (40 × 45) - 14 = 1800 - 14 = 1786. Actual average = 1786/40 = 44.65.

Multiple choice

The average of 22 numbers is 37.5. The average of first 12 numbers is 40.6 and that of the last 12 numbers is 35.4. If 11th and 12th numbers are excluded, then what is the average of the remaining numbers?
  1. $37.8$
  2. $37.4$
  3. $36.4$
  4. $36.9$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total sum of 22 numbers = 22 × 37.5 = 825. Sum of first 12 = 12 × 40.6 = 487.2. Sum of last 12 = 12 × 35.4 = 424.8. Since 11th and 12th are counted in both sets, their sum = 487.2 + 424.8 - 825 = 87. Sum of remaining 20 numbers = 825 - 87 = 738. Average = 738/20 = 36.9

Multiple choice

Richa travels from A to B at the speed of 15 km/h, from B to C at 20 km/h, and from C to D at 30 km/h If (AB = BC = CD), then find the Richa's average speed.

  1. 17 km/h

  2. 19 km/h

  3. 20 km/h

  4. 18 km/h
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When distances are equal, average speed is the harmonic mean: Average speed = Total distance ÷ Total time. Let distance = d. Time for each segment = d/15, d/20, d/30. Total time = d(1/15 + 1/20 + 1/30) = d(9/60) = 3d/20. Average speed = 3d ÷ (3d/20) = 20 km/h. Options A (17), B (19), and D (18) are incorrect because they use arithmetic mean or other wrong methods.

Multiple choice

The average weight of some students in a group is 58 kg. If 8 students of average weight 54 kg leave the group, and 3 students weighing 53.6 kg, 54 kg and 57.4 kg join the group, then the average weight of the remaining students in the group will increase by 575 g. The number of students, initially, in the group is

  1. 35

  2. 45

  3. 50

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

Let n be initial number of students. Total weight = 58n. After 8 leave and 3 join, new total = 58n - 8×54 + 53.6 + 54 + 57.4 = 58n - 432 + 165 = 58n - 267. New average: (58n - 267) ÷ (n - 5) = 58.575. Solving: 58n - 267 = 58.575(n - 5) = 58.575n - 292.875, which gives 0.575n = 25.875, so n = 45. Options A (35), C (50), and D (40) are incorrect.

Multiple choice

The average age of 125 students in a group is 16.2 years. 40% of the students are boys and the rest are girls. The average age of the boys is 20% more than the average age of the girls. What is the average age (in years) of the boys?

  1. 17

  2. 18.5

  3. 18

  4. 17.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the average age of girls be g years. Then the average age of boys is 1.2g (20% more). With 125 students (50 boys, 75 girls), total age = 50(1.2g) + 75g = 135g. The overall average is 135g/125 = 16.2, giving g = 15. Therefore, boys' average = 1.2 × 15 = 18 years. This uses the weighted average principle combined with the percentage relationship between the two averages.

Multiple choice

The average of ten numbers is 18.2. The average of the first four numbers is 16.6 and that of the last seven numbers is 20.8. If the 4th number is excluded, then the average of the remaining numbers is (correct to one decimal place):

  1. 16.9

  2. 15.8

  3. 17.2

  4. 16.7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sum of 10 numbers = 18.2 × 10 = 182. Sum of first 4 numbers = 16.6 × 4 = 66.4. Sum of last 7 numbers = 20.8 × 7 = 145.6. The 4th number is counted in both groups, so: Sum of all 10 + 4th number = 66.4 + 145.6 = 212. Therefore, 4th number = 212 - 182 = 30. Sum of remaining 9 numbers (excluding 4th) = 182 - 30 = 152. Average of remaining 9 numbers = 152/9 = 16.89 ≈ 16.9.

Multiple choice

The total of three numbers is 240. The second number is four times the first number. The third number is three times the first number. What will be the average of the three numbers and what is the third number?
  1. $80, 90$
  2. $70, 120$
  3. $50, 30$
  4. $60, 120$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the first number be x. Then second = 4x, third = 3x. Sum: x + 4x + 3x = 240, so 8x = 240, giving x = 30. The numbers are 30, 120, 90. Average = 240/3 = 80, and third number = 90. Option A matches both values correctly.

Multiple choice

In a class of 39 students, there are 26 girls. The average weight of these girls is 42Kgs and the average weight of the full class is 48kgs. What is the average weight (in kgs) of the boys in the class?

  1. 54

  2. 66

  3. 60

  4. 62
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total class weight = 39 × 48 = 1872 kg. Girls' total weight = 26 × 42 = 1092 kg. Number of boys = 39 - 26 = 13. Boys' total weight = 1872 - 1092 = 780 kg. Average weight of boys = 780 ÷ 13 = 60 kg.

Multiple choice

In an innings, the average of the first 6 batsmen is 50 , while that of the latter 5 batsmen is 20 . If the scores of three batsmen from the first lot and three from the latter are swapped, the average of its first six becomes 40 , then what would the average of latter five become?

  1. 32

  2. 28

  3. 25

  4. 30
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total runs from all 11 batsmen initially: 6×50 + 5×20 = 300 + 100 = 400. After swapping, average of first 6 is 40, so their total = 240. Since total runs remain 400, latter 5 total = 400 - 240 = 160, giving average = 160/5 = 32. The key insight is that swapping doesn't change the overall total. Option A is correct.