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

Bowling average of Jadeja in matches played by him was 14 runs/wicket. In next match his performance was 4 wickets for 72 runs. So his new bowling average becomes 14.2 runs/wicket. Find the total number of wickets taken by him till now.

  1. 72 wickets

  2. 80 wickets

  3. 76 wickets

  4. 84 wickets
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let w be wickets before the new match. Total runs conceded = 14w. After 4 wickets for 72 runs, new average = 14.2 = (14w + 72)/(w + 4). Cross-multiplying: 14.2(w + 4) = 14w + 72. This gives 14.2w + 56.8 = 14w + 72, so 0.2w = 15.2, and w = 76. Total wickets = 76 + 4 = 80.

Multiple choice

The average of 13 numbers is 47. The average of the first 3 numbers is 39 and the next 7 numbers is 49. The 11th term is twice the 12th term, and the 12th term is 3 more than the 13th term. Find the 11th term.
  1. $45.4$
  2. $45.6$
  3. $45.5$
  4. $45$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sum of all 13 numbers = 13 × 47 = 611. Sum of first 3 = 3 × 39 = 117. Sum of next 7 = 7 × 49 = 343. Sum of terms 11, 12, 13 = 611 - 117 - 343 = 151. Let x = 13th term. Then 12th term = x + 3, and 11th term = 2(x + 3) = 2x + 6. Sum: (2x + 6) + (x + 3) + x = 151. Solving: 4x + 9 = 151, so 4x = 142, and x = 35.5. Therefore 11th term = 2(35.5 + 3) = 45.5.

Multiple choice

The average age of a family of 8 members is 22 years. If the age of the youngest member be 8 years, the average age of the family at the birth of the youngest member was?

  1. 18 years

  2. 16 years

  3. 23 years

  4. 22 years

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

Current total age of 8 members = 8 × 22 = 176 years. At the birth of the youngest (8 years ago), each of the other 7 members was 8 years younger. Their ages 8 years ago totaled 176 - 8 - (7 × 8) = 176 - 8 - 56 = 112 years. Average age at that time = 112/7 = 16 years. The key insight: subtract 8 years from each of the 7 existing members' ages, then calculate the average.

Multiple choice

The average of the four numbers is 24.5. Out of the four numbers, the first is 1.5 times the second, the second is (\frac{1}{3}) rd of the third, and the third is 2 times the fourth number. Then what is the smallest of all these numbers?
  1. $12$
  2. $13$
  3. $14$
  4. $15$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given average = 24.5, sum of four numbers = 98. Let numbers be a, b, c, d. From conditions: a = 1.5b, b = c/3 (so c = 3b), and c = 2d (so d = c/2 = 1.5b). Substituting: 1.5b + b + 3b + 1.5b = 7b = 98, giving b = 14. The numbers are 21, 14, 42, 21, making 14 the smallest. Options A, B, D are incorrect as they don't satisfy the given relationships.

Multiple choice

During morning walk, a man covers respectively a distance of 6 km, 5.5 km, 4 km, 5 km and 4.5 km from Monday to Friday. How much distance should he cover on two more days, so that his average per week becomes 8 km per day?

  1. 30

  2. 31

  3. 32

  4. 21
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For an average of 8 km per day over 7 days, total distance needed is 7 × 8 = 56 km. Distance covered from Monday to Friday is 6 + 5.5 + 4 + 5 + 4.5 = 25 km. Remaining distance needed = 56 - 25 = 31 km. This 31 km must be covered over two days (Saturday and Sunday).

Multiple choice

The average score obtained by Subir in 15 tests is 29. Ruchira has so far scored an average of 27, but has given only 11 tests so far. How much does Ruchira score on average in the remaining four tests to match Subir's performance?

  1. 36

  2. 35.5

  3. 35

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

Subir's total = 15 × 29 = 435. Ruchira needs same total in 15 tests. Current total = 11 × 27 = 297. Needs 435 - 297 = 138 in remaining 4 tests. Average = 138/4 = 34.5.

Multiple choice

The average score of 132 students of the college is 40. If the average of the marks of the passed students is 42 and the average of the marks of unsuccessful students is 20, what will be the respective ratio of the total marks of the passed students and the total marks of the unsuccessful students?

  1. 21: 1

  2. 23: 2

  3. 19: 11

  4. 9: 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let P=passed students, F=failed students. Total: 132×40=5280 marks. Also: 42P+20F=5280 and P+F=132. Solving: 42P+20(132-P)=5280, so 22P=5280-2640=2640, P=120, F=12. Ratio of marks: (42×120):(20×12)=5040:240=21:1.

Multiple choice

The average weight of certain people in a family is 60 kg. If 5 new guests having weight 10%, 20%, 30% 40% and 50% respectively more than the average weight of the family join the family, then average weight of all people increased by 5 Kg. The number of persons in family after joining the guests are:

  1. 12

  2. 13

  3. 17

  4. 19

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

Let n be original family members. Original total = 60n. New guests weigh: 60(1.1), 60(1.2), 60(1.3), 60(1.4), 60(1.5). New total = 60n + 60(1.1+1.2+1.3+1.4+1.5) = 60n + 60(7.5) = 60n + 450. New average = (60n + 450)/(n + 5) = 65. Solving: 60n + 450 = 65n + 325, so 5n = 125, n = 25. Total after joining = 25 + 5 = 30. Since 30 is not in options, answer is None of these.

Multiple choice

What is the average weight of girls in the class? I. Average weight of all the 60 students is 42 kg. II. Average weight of boys is 43 kg. III. Total weight of all girls together is 1144 kg.

  1. Any two of the three

  2. All I, II & III

  3. Only I & II

  4. Only II & III

  5. Question cannot be answered even with the information in all the three statements
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

We need: (Total girls' weight) / (Number of girls) = ?. Let G = number of girls. From I: Total weight = 60 x 42 = 2520 kg. Boys = 60 - G. From II: Boys' avg = 43, so boys' total = 43 x (60 - G). From III: Girls' total = 1144 kg. Using all three: 2520 = 43(60 - G) + 1144. Solving: 2520 = 2580 - 43G + 1144, 43G = 2580 + 1144 - 2520 = 1204, G = 28. Girls' average = 1144/28 = 40.85 kg (approximately 41 kg). All three statements are necessary.

Multiple choice

The average marks of Rinku, Mohit and Suman is 65. Rinku's marks is 18 less than Alok and 12 more than Mohit. If Alok got 38 marks more than the average marks of Rinku, Mohit and Suman. Then what is the sum of marks of Mohit and Suman?

  1. 124

  2. 110

  3. 108

  4. 120
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let Rinku = R, Mohit = M, Suman = S. Average = 65 means R + M + S = 195. R = M + 12 (R is 12 more than M). Alok = R + 18 = M + 30. Alok's marks = 65 + 38 = 103. So M + 30 = 103, meaning M = 73. Then R = 73 + 12 = 85. S = 195 - 85 - 73 = 37. Sum of Mohit and Suman = 73 + 37 = 110. Option A (124) is incorrect. Option C (108) is incorrect. Option D (120) is incorrect.

Multiple choice

There are 100 students in 3 class VI, VII and VIII of a School. The average weight of all the three class taking together is 42 kg. The average weight of VII and VIII is 43.75 kg and the average weight of VI is 35. The number of students in VI is

  1. 20

  2. 35

  3. 30

  4. 25

  5. 24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let students in VI = v. Total students = 100, so students in VII and VIII = 100 - v. Total weight = 100 × 42 = 4200 kg. Weight of VII + VIII = (100-v) × 43.75. Weight of VI = v × 35. So: v×35 + (100-v)×43.75 = 4200. This gives 35v + 4375 - 43.75v = 4200, so -8.75v = -175, giving v = 20.

Multiple choice

There are 5 older and some children living in a family, thus the average age of their family is 28 years. If the average age of elders and children is 42 years and 18 years respectively, then how many children are there in the family?

  1. 5

  2. 8

  3. 7

  4. 6

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

Let number of children be x. Total people = 5 + x. Using weighted average: (5×42 + x×18)/(5 + x) = 28. Solving: 210 + 18x = 28(5 + x) = 140 + 28x. So 210 - 140 = 28x - 18x, giving 70 = 10x, therefore x = 7. There are 7 children in the family.