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 Aman, Akash and Avinash is 70 kg. Another person Sangram joins the group and now the average is 66 kg. If another person Ashish whose weight is 6 kg more than Sangram, joins the group replacing Aman, then average weight of Aman, Avinash, Sangram and Ashish becomes 75 kg. What is the weight of Akash (in kg)?

  1. 18

  2. 24

  3. 32

  4. 46

  5. 54
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Average of Aman, Akash, Avinash = 70, so their sum = 210. With Sangram (average 66), sum of 4 = 264, so Sangram = 54. Ashish = Sangram + 6 = 60. Average of Aman, Avinash, Sangram, Ashish = 75, so their sum = 300. Aman + Avinash + 54 + 60 = 300, so Aman + Avinash = 186. From Aman + Akash + Avinash = 210 and Aman + Avinash = 186, we get Akash = 24.

Multiple choice

In an exam of 100 marks, the average marks of a class of 40 students are 76. If the top 3 scorers of the class leave, the average score falls down by 1. If the other two toppers except “the highest topper scored not more than 85”. Then what is the minimum score the topper can score?

  1. 95

  2. 80

  3. 85

  4. 78

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

Total marks of 40 students = 76×40 = 3040. After 3 toppers leave, 37 students have average 75, so total = 75×37 = 2775. Sum of 3 toppers' marks = 3040-2775 = 265. If two toppers scored at most 85 each (maximum possible), the third topper scored at least 265-85-85 = 95. This is the minimum possible score.

Multiple choice

In 6 days of a week, 250 boys attended for the first four days and 260 boys for the last three days. The average attendance in this week is 255. The number of students present on Thursday was-
  1. $260$
  2. $250$
  3. $240$
  4. $280$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First 4 days: 250 boys/day = 250×4 = 1000. Last 3 days: 260 boys/day = 260×3 = 780. But this double-counts days 4, 5, 6 (Thursday, Friday, Saturday). Total week = 6 days, average = 255, so total = 255×6 = 1530. Let Thu = x. Then: Mon+Tue+Wed+Thu+Fri+Sat = 1530, so 250+250+250+x+260+260 = 1530, giving 1270+x = 1530, so x = 260. Wait - this gives x=260, but claimed answer is 250. Let me recalculate: First 4 days = Mon, Tue, Wed, Thu (at 250 each = 1000). Last 3 days = Thu, Fri, Sat (at 260 each = 780). Total count including Thursday twice = 1780. Actual total = 1530. Thursday counted twice, so 1780 - Thu = 1530, Thu = 250. Correct! The claimed answer is indeed correct.

Multiple choice

Average age of a volleyball team having 6 players is 21 years. If the age of the coach is also included, then the average age increases by 3.5 years. What is the age (in years) of the coach?

  1. 38.5

  2. 39.5

  3. 45.5

  4. 40.5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total age of 6 players = 6 × 21 = 126 years. When coach is included, new average = 21 + 3.5 = 24.5 years for 7 people. Total with coach = 7 × 24.5 = 171.5 years. Coach's age = 171.5 - 126 = 45.5 years.

Multiple choice

The average age of 39 students and the principal is 18 years. When the principal's age is excluded, the average age decreases by 1 year. What is the age of principal?

  1. 57 years

  2. 60 years

  3. 58 years

  4. 48 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total of 40 people (39 students + principal) have average age 18, so sum = 40 × 18 = 720 years. When principal is excluded, 39 students have average 17, so their sum = 39 × 17 = 663 years. Principal's age = 720 - 663 = 57 years. This works because removing the principal reduces the average by exactly 1 year.

Multiple choice

The average weight of first 11 persons among 12 persons is 95 kg. The weight of 12th person is 33 kg more than the average weight of all the 12 persons. The weight of the 12th person is

  1. 128 kg

  2. 97.45 kg

  3. 128.75 kg

  4. 131 kg
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let average of all 12 be x. Total of first 11 = 11 × 95 = 1045. Total of all 12 = 12x. So 12th person = 12x - 1045. Given: 12th person = x + 33. So 12x - 1045 = x + 33, giving 11x = 1078, so x = 98. Thus 12th person = 98 + 33 = 131 kg.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? How much marks did Jitendra get in an examination? (I) Average marks of all students excluding Jitendra is 88 whereas average marks of all students including Jitendra is 89. (II) Average marks of all students excluding Jitendra and Umesh is 87.9.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient

  5. If both statements together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement I gives us two equations but introduces unknowns: let n be total students and J be Jitendra's marks. We get S = 88(n-1) and S+J = 89n, which simplifies to J = n + 88. Without knowing n (total students), we cannot find J. Statement II gives average excluding Jitendra AND Umesh as 87.9, introducing yet another unknown (Umesh's marks). Even combining both statements, we have insufficient information to determine Jitendra's marks uniquely.

Multiple choice

The average score of a class of boys and girls in an examination is N. The ratio of boys and girls in the class is 4 : 1.If the average score of the boys is (N + 1), then the average score of the girls is- एक परीक्षा में एक कक्षा के लड़को और लड़कियो का औसत स्कोर N है। कक्षा में लड़को और लड़कियों का अनुपात 4 : 1 है । यदि लड़को का औसत स्कोर (N + 1) हो ,तो लड़कियों का औसत स्कोर है-

  1. (N – 1)

  2. (N – 2)

  3. (2N + 1)

  4. (N – 4)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using weighted average: Total score = 4b × (N+1) + b × G = 5b × N. Solving: 4N + 4 + G = 5N, so G = N - 4. The girls' average must be lower than the overall average since boys score above average.

Multiple choice

Average of 13 numbers is 58, the average of Ist 7 numbers is 63 and the average of last 7 numbers is 70. Find the 7th number.
  1. $167$
  2. $77$
  3. $187$
  4. $177$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The sum of first 7 numbers is 7 × 63 = 441. The sum of last 7 numbers is 7 × 70 = 490. The total sum of all 13 numbers is 13 × 58 = 754. The 7th number is counted in both groups, so: 441 + 490 - 7th number = 754. Therefore, 7th number = 441 + 490 - 754 = 177. This is a weighted average problem where the overlapping element must be subtracted.

Multiple choice

The average age of a class was 15 years.When 5 boys whose average age was 12 years and 6 months were admitted in the class, the average was reduced to 6 months.How many students were there in the class originally?

  1. 20

  2. 24

  3. 25

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

Let n be the original number of students. Total age = 15n. 5 new boys add 5 × 12.5 = 62.5 years. New average = (15n + 62.5)/(n+5) = 14.5. Solving: 15n + 62.5 = 14.5n + 72.5, so 0.5n = 10, giving n = 20 students.

Multiple choice

A question and some statements are given below it. You have to decide whether the data provided in the statements is sufficient to answer the question. You should use the given data and your knowledge of Mathematics to choose between the possible answers. What is the Weight of the Teacher? I. There are 24 students in the class. II. The average weight of students and the professor is 64 Kg. III. The average weight of the professor and students is 2 Kg more than that of students

  1. The data in both the statement I and II together is sufficient to answer the question, while the data in statement III alone is not sufficient to answer the question.

  2. The data in both the statement II and III together is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. The data in both the statement I and III together is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  4. The data given in all statements I, II and III together are necessary to answer the question.

  5. The data given in all statements I, II and III are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Statements give: 24 students, average of (students + teacher) = 64kg, and professor + students average is 2kg more than students alone. This gives relationships but no actual weight values. We can find that teacher's weight exceeds student average by (24 × 2) = 48kg, but without knowing the actual student average weight, we cannot determine teacher's absolute weight.

Multiple choice

The average of thirteen numbers is 80. The average of the first five numbers is 74.5 and that of the next five numbers is 82.5. The 11th number is 6 more than the 12th number and the 12th number is 6 less than the 13th number. What is the average of the 11th and 13th numbers?
  1. $87$
  2. $54$
  3. $85$
  4. $86$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total sum = 13 × 80 = 1040. Sum of first 10 numbers = 5 × 74.5 + 5 × 82.5 = 372.5 + 412.5 = 785. Sum of 11th, 12th, 13th = 1040 - 785 = 255. Let 12th = x, then 11th = x + 6, 13th = x + 6. So (x + 6) + x + (x + 6) = 255, giving 3x = 243, x = 81. Average of 11th and 13th = (87 + 87)/2 = 87.

Multiple choice

The average marks of some students in a class is 43. When 4 students are included the average becomes 42.5 and the marks of those 4 students are 42, 36.5, 39 and 42.5 in the class. The number of students in the class was ?

  1. 15

  2. 20

  3. 25

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

Let n be original students. Total marks = 43n. Adding 4 students with marks 42+36.5+39+42.5 = 160 gives: (43n+160)/(n+4) = 42.5. Solving: 43n+160 = 42.5n+170, so 0.5n = 10, n = 20. So there were 20 students originally.