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

Average weight of three friends Amar, Raman and Daman is 70 kg. Another person Vishal joins the group and now the average is 66 kg. If another person Tahir whose weight is 6 kg more than Vishal, joins the group replacing Amar, then average weight of Raman, Daman, Vishal and Tahir becomes 75 kg. What is the weight of Amar (in kg)?

  1. 18

  2. 20

  3. 22

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

Amar, Raman, Daman average 70 kg means total = 210 kg. With Vishal, average 66 kg for 4 people means total = 264 kg, so Vishal = 54 kg. Tahir = Vishal + 6 = 60 kg. New group (Raman, Daman, Vishal, Tahir) average 75 kg means total = 300 kg. So Raman + Daman + 54 + 60 = 300, giving Raman + Daman = 186 kg. From original: Amar + 186 = 210, so Amar = 24 kg.

Multiple choice

There are 10 compartments in a passenger train that carries an average (15) passengers per compartment. If at least (7) passengers were sitting in each compartment, no compartment has an equal number of passengers, and any compartment does not exceed the number of average passengers except the 10th compartment. Find how many passengers can be accommodated in the 10th compartment.

  1. 38

  2. 51

  3. 47

  4. 50
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Compartments 1-9 must have distinct values from 7 to 15 (inclusive), with all different and each at least 7. The maximum sum for 9 compartments under 15 is 7+8+9+10+11+12+13+14+15 = 99. Total passengers = 10 × 15 = 150. The 10th compartment = 150 - 99 = 51.

Multiple choice

Average age of a football team having 11 players is 22 years. If the age of the coach is also included, then the average age increases by 3 years. What is the age (in years) of the coach?

  1. 48

  2. 52

  3. 56

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

Total age of 11 players = 11×22 = 242 years. With coach, average increases by 3 years to 25 years for 12 people. Total age becomes 12×25 = 300 years. Coach's age = 300 - 242 = 58 years. This is a standard average problem requiring setting up the equation carefully.

Multiple choice

The average marks obtained by S in 15 tests is 29. R is maintaining an average of 27 so far but has taken only 11 of the tests so far. How much does R have to score on an average in the remaining four tests to match S's performance?

  1. 36

  2. 35.5

  3. 35

  4. 34.5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

S's total marks after 15 tests is 29 x 15 = 435. R has scored 27 x 11 = 297 marks in 11 tests. To match S's total, R needs 435 - 297 = 138 more marks across 4 remaining tests. Required average = 138/4 = 34.5. This accounts for the total needed rather than just matching the average.

Multiple choice

The average weight of 40 Students is 32. If the Heaviest and Lightest are excluded the average weight reduces by 1. If only the Heaviest is excluded then the average is 31. Then what is the weight of the Lightest?

  1. 30

  2. 31

  3. 32

  4. 33

  5. 34
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total weight = 40 × 32 = 1280. Without heaviest and lightest: 38 × 31 = 1178, so heaviest + lightest = 102. Without heaviest: 39 × 31 = 1209, so heaviest = 1280 - 1209 = 71. Therefore, lightest = 102 - 71 = 31.

Multiple choice

The average weight of Sanjay, Mohan and Charu is 80 kg. Kamal joins them and the average weight of the four becomes 81 kg. If Ram whose weight is 2 kg more than Kamal replaces Sanjay, then the average weight of Mohan, Charu, Kamal and Ram becomes 83 kg. Find the weight of Sanjay?

  1. 80

  2. 85

  3. 78

  4. 70

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sanjay + Mohan + Charu = 80 × 3 = 240 kg. Adding Kamal: (240 + Kamal)/4 = 81, so Kamal = 324 - 240 = 84 kg. Ram = Kamal + 2 = 86 kg. New average: Mohan + Charu + Kamal + Ram = 83 × 4 = 332 kg. Substituting: (240 - Sanjay) + 84 + 86 = 332, so Sanjay = 410 - 332 = 78 kg.

Multiple choice

The average weight of 3 students P, Q and R is 84kg. Another student S joins the group and the average becomes 80kg. If another man T whose weight is 3kg more than that of S, replaces P, then the average weight of Q, R, S and T becomes 79 kg then the weight of P is

  1. 75

  2. 82

  3. 45

  4. 98

  5. 88
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

P + Q + R = 3 × 84 = 252kg. When S joins: P + Q + R + S = 4 × 80 = 320kg. Therefore S = 320 - 252 = 68kg. T's weight = S + 3 = 71kg. Q + R + S + T = 4 × 79 = 316kg. So Q + R = 316 - (68 + 71) = 177kg. Then P = (P + Q + R) - (Q + R) = 252 - 177 = 75kg. Option A is correct.

Multiple choice

If the average weight of the whole class is 50 kg. And the average weight of boys in the class is 60 kg and the average weight of girls in the same class is 44 kg. What could be the possible ratio of strength of boys and girls in the class respectively?

  1. 2: 3

  2. 3: 4

  3. 4: 5

  4. 3: 5

  5. 1: 2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using weighted average formula: Average = (b×60 + g×44)/(b+g) = 50. So 60b + 44g = 50(b+g), 60b + 44g = 50b + 50g, 10b = 6g, b:g = 6:10 = 3:5. Option D (3:5) satisfies: (3×60 + 5×44)/(3+5) = (180 + 220)/8 = 400/8 = 50. Option A gives 52, B gives 51.43, C gives 50.89, E gives 52 - none equal 50.

Multiple choice

A class consists of students whose average weight is 65.5. Four students of 72.2 kg, 70.3 kg, 67.7 kg and 70.8 kg, joined the class and the average weight increased by 500 gms. Find the number of students initially.

  1. 26

  2. 30

  3. 34

  4. 32
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The correct answer is C because let n be the initial number of students. Total initial weight = 65.5n. Four students join with weights 72.2 + 70.3 + 67.7 + 70.8 = 281 kg. New average = 65.5 + 0.5 = 66 kg for (n + 4) students. Equation: (65.5n + 281)/(n + 4) = 66. Solving: 65.5n + 281 = 66n + 264, so 0.5n = 17, giving n = 34.

Multiple choice

The average marks scored by a student in 5 subjects is 75. The average marks scored by him in the first two subjects is 65. The average marks scored by him in the last two subjects is 85. How many marks did the student score in the third subject?

  1. 80 marks

  2. 70 marks

  3. 65 marks

  4. 75 marks
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total marks in 5 subjects = 5 × 75 = 375. Sum of first 2 = 2 × 65 = 130. Sum of last 2 = 2 × 85 = 170. Third subject marks = 375 - 130 - 170 = 75. Option D matches.

Multiple choice

Average age of 9 men is 45 years. If the age of one woman is included, then the average age becomes 44 years. What is the age of the woman?

  1. 44 years

  2. 30 years

  3. 40 years

  4. 35 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Average of 9 men = 45 years, so total age = 9×45 = 405 years. When woman is added, average of 10 people = 44 years, so total = 10×44 = 440 years. Therefore woman's age = 440-405 = 35 years. The average decreases because the woman's age is below the original average.

Multiple choice

The average of fifteen person is 32 years. If two more persons are added then the average is increased by 3 years. The new person have an age difference of 7 years between them. The age (in year) of the older among the new persons is?

  1. 58

  2. 61

  3. 50

  4. 54
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total age of 15 persons = 15 × 32 = 480 years. After adding 2 persons, total becomes 17 × 35 = 595 years. Sum of ages of the 2 new persons = 595 - 480 = 115 years. Let the ages be x and y with x > y. Given x - y = 7 and x + y = 115. Solving: 2x = 122, so x = 61 years. The older person is 61 years old.