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

There were 9 boys and some girls in one class. In an examination, boys scored 13 average marks, while girls had an average score of 15. If the total average of the marks is 14.28, then what will be the total number of students in the class?

  1. 27

  2. 26

  3. 24

  4. 25
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let number of girls be g. Total marks for boys: 9 × 13 = 117. Total marks for girls: 15g. Combined average: (117 + 15g)/(9 + g) = 14.28. Solving: 117 + 15g = 128.52 + 14.28g, giving 0.72g = 11.52, so g = 16. Total students = 9 + 16 = 25.

Multiple choice

The average of 16 numbers is 48. The average of the first seven numbers is 45 and the average of the next 6 numbers is 52. If 14th number is 11 less than 15th number and 5 more than 16th number , Then the average of 15th and 16th numbers is ?

  1. 47.5

  2. 48.5

  3. 49

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

Total sum of 16 numbers = 16 × 48 = 768. Sum of first 7 numbers = 7 × 45 = 315. Sum of next 6 numbers = 6 × 52 = 312. So sum of 14th, 15th, and 16th numbers = 768 - 315 - 312 = 141. Given: a14 = a15 - 11 and a14 = a16 + 5. So a16 = a14 - 5 = a15 - 16. Then a14 + a15 + a16 = (a15 - 11) + a15 + (a15 - 16) = 3a15 - 27 = 141, giving a15 = 56. Then a16 = 56 - 16 = 40. Average of 15th and 16th = (56 + 40) / 2 = 48.

Multiple choice

The average weight of 10 students is 80 kg. If the heaviest and the lightest weights are not considered, the average is 81 kg. If the heaviest weight is 92 kg, find the lightest weight.

  1. 50

  2. 60

  3. 70

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

Total weight of 10 students = 10 × 80 = 800 kg. Excluding heaviest (92 kg) and lightest (x), average of 8 students = 81 kg, so their total = 8 × 81 = 648 kg. Therefore 92 + x = 800 - 648 = 152, so x = 152 - 92 = 60 kg.

Multiple choice

45 is the average marks obtained by 30 students of a class. On rechecking, two errors were identified. On correction, one student obtained 45 more marks while other obtained 15 less marks. What is the average of corrected marks?

  1. 45

  2. 44

  3. 47

  4. 46
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total marks for 30 students = 30 × 45 = 1350. After rechecking, one student gains 45 marks and another loses 15 marks. Net change = +45 - 15 = +30. New total = 1350 + 30 = 1380. New average = 1380 ÷ 30 = 46.

Multiple choice

There is a group of 8 lions. One lion leaves the group and a new lion joins the group. Due to this, average age of lions becomes same as the average 2 years ago. If the member left was aged 42. Then what is the age of new lion?

  1. 22

  2. 28

  3. 24

  4. 26
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When one lion leaves and another joins, keeping the group size at 8, the average returns to what it was 2 years ago. This means the new lion's age must be 2 years younger than the lion who left, since the group collectively 'lost' 8 years (8 lions × 2 years = 16 years) to reverse 2 years of aging. If the departed lion was 42, the new lion is 42 - 16 = 26.

Multiple choice

The average weight of 3 persons P, Q, R is 84 kg. Another person who is S joins the group and now the present average of the group becomes 80 kg. If another person T, whose weight is 3 kg more than that of S, replaces P then the average weight of Q, R, S, and T becomes 78 kg. Find the weight of P.

  1. 58 kg.

  2. 61 kg.

  3. 79 kg.

  4. 57 kg.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

P+Q+R = 3×84 = 252kg. When S joins: P+Q+R+S = 4×80 = 320kg, so S = 320-252 = 68kg. T is 3kg more than S, so T = 71kg. New average 78kg for Q,R,S,T means total = 4×78 = 312kg. So Q+R = 312 - (68+71) = 173kg. Then P = 252 - 173 = 79kg.

Multiple choice

The average of 10 numbers is 53 if the average of the first 4 numbers is 63 and the average of the last 4 numbers is 47, then the average of the remaining two numbers will be ?

  1. 45

  2. 90

  3. 47

  4. 53

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

Total of 10 numbers = 10 × 53 = 530. Sum of first 4 = 4 × 63 = 252. Sum of last 4 = 4 × 47 = 188. Sum of remaining 2 numbers = 530 - 252 - 188 = 90. Average of remaining 2 = 90/2 = 45. This uses the weighted average principle.

Multiple choice

Average weight of a class consisting 24 students is 47.25 kg. When two students leave the class new average is decreased by 0.25 kg. If weight of first students was 49 kg, find the weight of other student. (in kg)

  1. 47

  2. 49

  3. 51

  4. 53

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

Original total weight = 24 × 47.25 = 1134 kg. New total weight = 22 × 47 = 1034 kg (since new average decreases by 0.25 kg). Combined weight of two leaving students = 1134 - 1034 = 100 kg. First student weighs 49 kg, so second student weighs 100 - 49 = 51 kg. Answer is C (51).

Multiple choice

What is the average weight of boys in the class? I. Average weight of all the 60 students is 45 kg. II. Average weight of girls is 50 kg. III. Total weight of all the boys together is 1250 kg.

  1. Only II and III

  2. I and either II or III

  3. Any two of these

  4. All I, II and III

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

From statement I: Total weight of 60 students = 60 × 45 = 2700 kg. From statement III: Total weight of boys = 1250 kg. So weight of girls = 2700 - 1250 = 1450 kg. From statement II: Average weight of girls = 50 kg, so number of girls = 1450/50 = 29. Number of boys = 60 - 29 = 31. Average weight of boys = 1250/31 ≈ 40.32 kg. All three statements are needed.

Multiple choice

What will be the total average weight of all children in school? Statement I: The average weight of boys in school is 55 kg. Statement II: The average weight of girls in school is 49 kg. Statement III: The number of boys in the school is 30% more than the number of girls.

  1. Only III

  2. All of the necessary

  3. Only II and III

  4. Only I and II

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

To find total average weight, we need weighted average: (total boys weight + total girls weight) / (total boys + total girls). Statement I gives boys' average = 55. Statement II gives girls' average = 49. Statement III gives boys = 1.3×girls. Using all three: Let girls = g, boys = 1.3g. Total average = (55×1.3g + 49×g) / (1.3g + g) = (71.5g + 49g) / 2.3g = 120.5/2.3 ≈ 52.4 kg. All three statements are necessary.

Multiple choice

The average of 24 numbers is 65. The average of first 11 numbers is 67 and the average of last 10 numbers is 70. If the 12th number is 13 less than the 13th number, and the 14th number is one more than the 13th number, then the average of 12th and 14th number is –

  1. 39

  2. 42

  3. 43

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

Total sum = 24 × 65 = 1560. Sum of first 11 = 11 × 67 = 737. Sum of last 10 = 10 × 70 = 700. Sum of positions 12, 13, 14 = 1560 - 737 - 700 = 123. Let 13th number = x. Then 12th = x - 13, 14th = x + 1. So (x-13) + x + (x+1) = 123, giving 3x - 12 = 123, so 3x = 135, x = 45. Average of 12th and 14th = (32 + 46)/2 = 78/2 = 39. This tests weighted average concepts and algebraic reasoning.

Multiple choice

The average presence of students of a class in a College on Monday, Tuesday and Wednesday is 16 and on the Wednesday, Thursday, Friday and Saturday is 15. If the average number of students on all the six days is 13 then the number of students who attended the class on Wednesday is?

  1. 30

  2. 28

  3. 38

  4. 40

  5. 20
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of students for Monday-Tuesday-Wednesday is 48, and for Wednesday-Thursday-Friday-Saturday is 60. The total for all six days is 78. Wednesday is counted in both averages, so 48 + 60 - Wednesday = 78, giving Wednesday = 30 students.