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 age of 160 boys in a class is 15 years. The average age of a group of 30 boys in the class is 16 years and the average age of another 50 boys in the class is 14 years. What is the average age of the remaining boys in the class?
  1. $15.25$
  2. $15.50$
  3. $15$
  4. $16.25$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total age of all 160 boys = 160 × 15 = 2400 years. Sum of ages for first 30 boys = 30 × 16 = 480 years. Sum for next 50 boys = 50 × 14 = 700 years. Remaining boys = 160 - 30 - 50 = 80 boys with total age = 2400 - 1180 = 1220 years. Their average = 1220/80 = 15.25 years. This uses the weighted average principle.

Multiple choice

The average of two numbers is 10 and the product of two numbers is 96. Find the two numbers?
  1. $3, 32$
  2. $12, 8$
  3. $1, 96$
  4. $24, 4$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the numbers be x and y. If average is 10, then (x+y)/2 = 10, so x+y = 20. If product is 96, then xy = 96. Substituting y = 20-x into xy = 96 gives x(20-x) = 96, so -x² + 20x - 96 = 0, or x² - 20x + 96 = 0. Solving: (x-8)(x-12) = 0, so numbers are 8 and 12. This can also be found by checking factor pairs of 96 that sum to 20.

Multiple choice

Average weight of group of 11 students is 37 kg. When a student left the group, then average weight of the group becomes 35 kg. What is the weight (in kg) of the student who left?

  1. 65

  2. 59

  3. 57

  4. 70
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total weight of 11 students = 11 × 37 = 407 kg. After one leaves, total weight of 10 students = 10 × 35 = 350 kg. The difference gives the weight of the student who left: 407 - 350 = 57 kg. This method uses average = total/count.

Multiple choice

Average of 11 numbers is 36, whereas average of 9 of them is 34. If the remaining two numbers are in the ratio 2: 3, then find the smaller number (between remaining two numbers).

  1. 54

  2. 24

  3. 30

  4. 36

  5. 48
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum of 11 numbers = 11 × 36 = 396. Sum of 9 numbers = 9 × 34 = 306. Sum of remaining 2 numbers = 396 - 306 = 90. In ratio 2:3, parts are 2x + 3x = 90, so 5x = 90, x = 18. Numbers are 36 and 54. Smaller is 36. Option D is correct.

Multiple choice

The average age of fifteen persons is 28 years. If two more persons are added, then the average is increased by 2 years. The new persons have age difference of 8 years. The age (in years) of the younger among the new persons is:

  1. 49

  2. 51

  3. 44

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

Total age of 15 persons = 15 × 28 = 420 years. After adding 2 persons, total age of 17 persons = 17 × 30 = 510 years. Sum of new persons' ages = 510 - 420 = 90 years. Let younger person's age = x, then older = x + 8. So x + (x + 8) = 90, giving 2x = 82, x = 41 years (option D).

Multiple choice

In a collage, the total age of 75 professors is 2160. The average age of 25 professors is 24 years and the average age of another 25 professors is 30. Find the average age of remaining professors.

  1. 32.4

  2. 36.5

  3. 25.4

  4. 28.2

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

Total age for 75 professors = 2160. First 25: average 24, total = 25 × 24 = 600. Next 25: average 30, total = 25 × 30 = 750. Remaining 25 professors: total = 2160 - 600 - 750 = 810. Average = 810/25 = 32.4 years.

Multiple choice

The average of (n) numbers is (a). If 2 is added to the first number, 4 is added to the second number, 8 is added to the third number, and each number of this type is added in the same order. Find the new average?
  1. $\(a + \frac{2(2^n - 1)}{n}\)$
  2. $\(a + \frac{2(1 - 2^n)}{n}\)$
  3. $\(n + \frac{2(1 - 2^n)}{n}\)$
  4. $\(a + \frac{2(1 - 2^n)}{a}\)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Original sum = na. The numbers added form a geometric progression: 2, 4, 8, 16, ..., 2^n. Sum of this GP = 2(2^n - 1)/(2 - 1) = 2(2^n - 1). New sum = na + 2(2^n - 1). New average = [na + 2(2^n - 1)]/n = a + 2(2^n - 1)/n.

Multiple choice

The average weight of A, B, C is 84 kg. If the weight of D is added, the average weight becomes 80 kg. If another person E, whose weight is 3 kg more than D, comes in place of A, then the average weight of B, C, D, E becomes 79 kg. Find the weight of A?

  1. 75

  2. 78

  3. 72

  4. 74
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A + B + C = 3 × 84 = 252 kg. Adding D: A + B + C + D = 4 × 80 = 320 kg. So D = 320 - 252 = 68 kg. E = D + 3 = 71 kg. Also, B + C + D + E = 4 × 79 = 316 kg. So B + C = 316 - 68 - 71 = 177 kg. Therefore, A = 252 - 177 = 75 kg.

Multiple choice

The average marks of 20 students in a test is 75. Later it is found that three marks 53, 60 & 76 were wrongly entered as 93, 64 & 86. The average marks after mistakes were rectified is

  1. 72.3

  2. 72.2

  3. 71.6

  4. 71.8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Original sum = 20 × 75 = 1500. Wrongly entered marks: 93 + 64 + 86 = 243. Correct marks: 53 + 60 + 76 = 189. Corrected sum = 1500 − 243 + 189 = 1446. Corrected average = 1446 ÷ 20 = 72.3. The net decrease is (243 − 189) ÷ 20 = 2.7, so 75 − 2.7 = 72.3.

Multiple choice

The ratio of marks obtained by Deepak and Naimish is 6:5. If the combined average of their percentage is 68.75 and their sum of the marks is 275, find the total marks for which exam was conducted.

  1. 200

  2. 250

  3. 300

  4. 350

  5. 275
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let marks be 6x and 5x. Sum = 11x = 275, so x = 25. Deepak = 150, Naimish = 125. Average percentage = 68.75%, so (150 + 125)/2 = 137.5 is 68.75% of total marks. Total marks = 137.5/0.6875 = 200. Check: 150/200 = 75%, 125/200 = 62.5%, average = 68.75%. Verified.

Multiple choice

A person receives 3 packages of average weight of 150 grams in January and 5 packages of average weight of 250 grams in February. What is the average weight in grams of all the packages received by the person in both months?

  1. 175 grams

  2. 212.5 grams

  3. 252.5 grams

  4. 200 grams
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total weight = (3 × 150) + (5 × 250) = 450 + 1250 = 1700 grams. Total packages = 3 + 5 = 8. Average = 1700/8 = 212.5 grams. Option B is correct.