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

In a class average marks scored by 40 students is 86. When 5 highest maeks are excluded the average reduced by 1 mark, find the average of 5 highest students.

  1. 92

  2. 96

  3. 93

  4. 97
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total marks for 40 students: 40 × 86 = 3440. Removing 5 highest: 35 × 85 = 2975. Sum of 5 highest = 3440 - 2975 = 465. Average of 5 highest = 465 ÷ 5 = 93. The average drop of 1 mark for remaining students means the removed group scored significantly higher.

Multiple choice

Average age of A, B and C is 84 years. When D joined average becomes 80 years. A new person E who is 4 years older than D comes at place of A average age of B, C, D and E becomes 78 years. What is the age of A?

  1. 50 years

  2. 60 years

  3. 70 years

  4. 80 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A+B+C का औसत = 84, इसलिए A+B+C = 84×3 = 252। D के आने पर औसत 80 हो जाता है, तो A+B+C+D = 80×4 = 320। इससे D = 320−252 = 68। E, D से 4 वर्ष बड़ा है, तो E = 68+4 = 72। B,C,D,E का औसत 78 है, इसलिए B+C+68+72 = 78×4 = 312। इससे B+C = 312−140 = 172। A की आयु = 252−172 = 80 वर्ष। विकल्प D सही है।

Multiple choice

The average of 11 observations is 78. If the average of first six results is 69 and that of the last six is 82 marks, then the sixth observation is -

  1. 54

  2. 48

  3. 40

  4. 45

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

Let the 11 observations be a1,a2,...,a11. Total sum = 11×78 = 858. Sum of first 6 = 6×69 = 414. Sum of last 6 = 6×82 = 492. The 6th observation is counted in both sums. So a6 = (414 + 492) - 858 = 906 - 858 = 48. Option B is correct.

Multiple choice

The average weight of 10 students is 80 kg. If the highest and the lowest weights are not considered, the average is 81 kg. If the highest weight is 92 kg, find the lowest– 10 छात्रों का औसत भार 80 किग्रा. है। यदि सबसे अधिक भार वाले छात्र को और सबसे कम भार वाले छात्र को सम्मिलित नहीं किया जाता है, औसत 81 किग्रा. हो जाता है। यदि सबसे अधिक भार 92 किग्रा. है, सबसे कम भार है-

  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 x 80 = 800 kg. Removing highest (92) and lowest (x), the remaining 8 have average 81, so their total = 8 x 81 = 648 kg. Therefore 92 + x = 800 - 648 = 152, which gives 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? एक कक्षा के 30 छात्रों के औसत अंक 45 हैं। पुनः निरीक्षण करने पर, दो त्रुटियाँ प्राप्त की गयी। सही करने पर, एक छात्र 45 अंक अधिक प्राप्त करता है जबकि दूसरा छात्र 15 अंक कम प्राप्त करता है। सही अंकों का औसत क्या है ?

  1. 45

  2. 44

  3. 47

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

The original total marks for 30 students is 30 × 45 = 1350. After correction, one student gains 45 marks and another loses 15 marks, resulting in a net change of +30 marks. The new total is 1350 + 30 = 1380. The corrected average is 1380 ÷ 30 = 46. Options A (45), B (44), and C (47) are incorrect because they don't account for both corrections properly.

Multiple choice

The average age of a cricket team of 11 players is the same as it was 3 years back because 3 of the players whose current average age is 33 years were replaced by 3 youngsters. The average age of the newcomers is

  1. 23 years

  2. 21 years

  3. 22 years

  4. 20 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original average age = a, so original sum = 11a। After 3 years, sum would be 11a + 33 (each of 11 players ages 3 years)। But 3 old players (avg 33) replaced by 3 youngsters (avg x), so current sum = 11a + 33 - 99 + 3x = 11a + 3x - 66। Given new average = a, so 11a = 11a + 3x - 66, solving: 3x = 66, x = 22 years। The team average remained same because the sum of ages of 3 old players (99) equals sum of ages of 3 new players plus the 3-year aging of remaining 8 players (24)। So new players avg = 99 - 24 / 3 = 22।

Multiple choice

A group of boys has an average weight of 42.75 kg. If one boy weighing 53 kg leaves the group and another boy weighing 36 kg joins the group then the average now becomes 42.25 kg .How many boys are there in the group? लड़कों के एक समूह का औसत भार 42.75 किलोग्राम है। यदि 53 किलोग्राम वजन का एक लड़का समूह छोड़ देता है तथा उसके स्थान पर 36 किलोग्राम का एक नया लड़का समूह में शामिल हो जाता है तो नया औसत 42.25 किलोग्राम हो जाता है । समूह में कितने लड़के हैं?

  1. 30

  2. 32

  3. 34

  4. 40
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let n be the number of boys initially. Total weight = 42.75n. When one boy of 53kg leaves and 36kg joins, total changes by -17 kg. New average: (42.75n - 17)/n = 42.25. Solving gives 0.5n = 17, so n = 34.

Multiple choice

Bowling average of a bowler was 16.8. In next match his performance was 93/5 thus his new bowling average becomes 17. Find the total runs considered by him before this match ?

  1. 650

  2. 545

  3. 840

  4. 745

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

Let initial runs = R and wickets = W. Given R/W = 16.8, so R = 16.8W. After the match, (R+93)/(W+5) = 17. Substituting: 16.8W + 93 = 17W + 85, giving 0.2W = 8, so W = 40. Initial runs = 16.8 × 40 = 672. Since 672 is not among options A-D, option E (None of these) is correct.

Multiple choice

The average age of a class was 15 years, when 5 boys whose average age was 12 years 6 months were admitted average of the class was reduced by 6 months. How many boys were there ? एक कक्षा की औसत आयु 15 वर्ष थी, जब 5 लड़के जिनकी औसत आयु 12 वर्ष 6 माह थी, शामिल किये जाते हैं, कक्षा का औसत 6 माह घट जाता है। वहां कक्षा में कितने लड़के थे?

  1. 20

  2. 170

  3. 270

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

Let original boys = n, total age = 15n. New total age = 15n + 5(12.5) = 15n + 62.5. New average = (15n + 62.5)/(n + 5) = 14.5. Solving: 15n + 62.5 = 14.5n + 72.5, so 0.5n = 10, n = 20.

Multiple choice

Average weight of a class is decreased by from 48 Kg to 47 Kg when 16 new students entered in class having average weight of 46.25 Kg. Find the number of students in the class initially. कक्षा का औसत वजन 48 किलो से कम होकर 47 किलोग्राम हो गया जब 16 नए छात्र कक्षा में प्रवेश करते हैं जिनका औसत वजन 46.25 किग्रा. था। प्रारम्भ में कक्षा में छात्रों की संख्या ज्ञात कीजिये।

  1. 8

  2. 24

  3. 30

  4. 12
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let n be initial number of students. Initial total weight = 48n. After 16 students join: total weight = 48n + 16 × 46.25 = 48n + 740. New average = (48n + 740)/(n + 16) = 47. So 48n + 740 = 47(n + 16) = 47n + 752. Therefore 48n - 47n = 752 - 740, giving n = 12. Initially there were 12 students.

Multiple choice

The average age of 40 students of a class is 15 years. When 10 new students are admitted, the average is increased by 0.2 years. The average age of the new students is - एक कक्षा में 40 छात्रों की औसत आयु 15 वर्ष है। जब 10 नये छात्र प्रवेश लेते है तो औसत में 0.2 वर्ष की वृद्धि हो जाती है। नये छात्रों की औसत आयु है-

  1. 15.2 years

  2. 16.0 years

  3. 16.2 years

  4. 15.8 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total age of 40 students = 40 * 15 = 600 years. After adding 10 students, total = 50 * 15.2 = 760 years. Sum of new 10 students' ages = 760 - 600 = 160. Their average = 160/10 = 16 years.