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 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 ? 39 छात्रों और प्रधानाचार्य की औसत उम्र 18 वर्ष है। जब प्रधानाचार्य की आयु को बाहर रखा गया है, औसत आयु में 1 वर्ष की कमी आती है तो प्रधानाचार्य की आयु क्या है ?

  1. 57 years/ वर्ष

  2. 60 years/ वर्ष

  3. 58 years/ वर्ष

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

Total age of 40 people = 40 × 18 = 720 years. Without principal, 39 students have average age of 17, so their total = 39 × 17 = 663 years. Principal's age = 720 - 663 = 57 years.

Multiple choice

There were 50 students in a hostel. If the number of students increases by 10, the expenses of the mess increase by Rs 180 while the average expenditure per head diminishes by Rs 1. Find the original expenditure of the mess? एक छात्रावास में 50 छात्र थे। यदि छात्रों की संख्या 10 बढ़ जाती है, तो भोजनालय का व्यय 180 रुपये बढ़ जाता है, जबकि प्रति व्यक्ति औसत व्यय 1 रुपये कम हो जाता है। तो छात्रावास में भोजन का मूल व्यय ज्ञात कीजिये?

  1. 1800

  2. 1600

  3. 1650

  4. 1200
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let original average expenditure be x rupees. Original total = 50x. When 10 students join, total = 60(x-1) = 60x - 60. This equals 50x + 180. So 60x - 60 = 50x + 180, giving 10x = 240, so x = 24. Original expenditure = 50 × 24 = Rs 1200. Option D is correct.

Multiple choice

The average marks of a student in 5 subjects was 76. In which the highest marks are 4 more than the second highest marks. If these two subjects are eliminated, the average marks of the remaining subjects are 72. What is the highest marks in a subject? 5 विषयों में एक विद्यार्थी के औसत अंक 76 थे । इनमे से अधिकतम अंक दूसरे सबसे अधिक अंक से 4 अधिक है । यदि इनमे से दो विषयों को निकाल दिया जाए, तो शेष विषयों का औसत अंक 72 हो जाता है। पांचो विषयों में से अधिकतम अंक कितने थे?

  1. 80

  2. 85

  3. 81

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

Total marks for 5 subjects = 5 × 76 = 380. Removing 2 subjects gives average 72 for 3 subjects, so their total = 3 × 72 = 216. The two removed subjects total = 380 - 216 = 164. Let second highest = x, then highest = x + 4. So x + (x + 4) = 164, giving 2x = 160, x = 80. Highest marks = 80 + 4 = 84.

Multiple choice

The average weight of A, B, C, D is 50 kg. A new person E join them; then he average weight of the group increased by 1 kg. Find the weight of E. A, B, C, D का औसत भार 50 किग्रा है। एक नया व्यक्ति E और आ जाता है तो औसत भार एक किग्रा बढ़ जाता है। व्यक्ति E का भार बताइए।

  1. 54 kg/किग्रा.

  2. 55 kg/किग्रा.

  3. 101 kg/किग्रा.

  4. 46 kg/किग्रा.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total weight of A, B, C, D = 4 × 50 = 200 kg. When E joins, new average = 51 kg for 5 people. Total weight of all 5 = 5 × 51 = 255 kg. E's weight = 255 - 200 = 55 kg. Option C (101 kg) would only be correct if average increased by 10 kg, not 1 kg.

Multiple choice

In the afternoon, a student read 100 pages at the rate of 60 pages / hour. In the evening, when he was tired, he read 100 more pages at the rate of 40 pages/hour. What was his average rate of reading in pages per hours?
  1. $48$
  2. $50$
  3. $60$
  4. $64$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Calculate the weighted average of reading speeds. In the afternoon: 100 pages at 60 pages/hour = 100/60 = 5/3 hours. In the evening: 100 pages at 40 pages/hour = 100/40 = 5/2 hours. Total pages = 200, total hours = 5/3 + 5/2 = (10+15)/6 = 25/6 hours. Average speed = Total pages / Total hours = 200 ÷ (25/6) = 200 × (6/25) = 8 × 6 = 48 pages/hour. Option A is correct.

Multiple choice

In an exam, the average was found to be 60 marks. After deducting an error, the marks of 80 students were found to have changed from 90 marks to 60 marks each. The average has also come down to 50 marks. Determine how many students have taken the exam?

  1. 360

  2. 240

  3. 120

  4. 250

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

Let n be total students. Initial total marks = 60n. After error correction, 80 students' marks changed from 90 to 60, meaning each lost 30 marks. Total marks deducted = 80 × 30 = 2400. New total = 60n - 2400 = 50n. Solving: 10n = 2400, so n = 240 students.

Multiple choice

Bowling average of Ishant sharma in 19 matches is 18 runs/ wicket . In next match his performance was 24 runs/ 2 wicket then his new bowling average becomes 17.5 runs/wicket. Find the total number of wickets taken by him till now.

  1. 21

  2. 25

  3. 32

  4. 24

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

Let total wickets before = w. Total runs before = 18 × w (since average = 18). In the new match: runs given = 24, wickets taken = 2. New total runs = 18w + 24, new total wickets = w + 2. New average = (18w + 24)/(w + 2) = 17.5. Solve: 18w + 24 = 17.5w + 35, so 0.5w = 11, w = 22. Total wickets now = w + 2 = 24.

Multiple choice

The average weight of 17 boys is 92 kg. If 18 new boys join the group, the average weight increases by 3 kg. What will be the average weight of the new 18 boys?
  1. $94.832 kg.$
  2. $95.73 kg.$
  3. $96.43 kg.$
  4. $98.83 kg.$
  5. $97.83 kg.$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The total weight of 17 boys = 17 × 92 = 1564 kg. When 18 new boys join, total boys = 35 and new average = 92 + 3 = 95 kg, so new total weight = 35 × 95 = 3325 kg. Weight of 18 new boys = 3325 - 1564 = 1761 kg. Their average = 1761/18 = 97.83 kg. Option E matches this value.

Multiple choice

The average height of the students in a class of 10 is 105 cm. If 20 more students with an average height of 120 cm join the class, what will be the average height of all students? एक कक्षा में 10 छात्रों की औसत ऊंचाई 105 सेमी. है। यदि 20 छात्र और 120 सेमी. औसत ऊंचाई के साथ जुड़ जाते है तो सभी छात्रों की औसत ऊंचाई क्या होगी?

  1. 115 cm. /सेमी.

  2. 110 cm. /सेमी.

  3. 112 cm. /सेमी.

  4. 114 cm. /सेमी.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

First group: total height = 10 × 105 = 1050 cm. Second group: total height = 20 × 120 = 2400 cm. Combined: (1050 + 2400) ÷ 30 = 3450 ÷ 30 = 115 cm.

Multiple choice

In a class of 65 students there are 39 girls. The average weight of these girls is 60 kg and average weight of the whole class is 64 kg. What is the average weight of the boys of the class ? विद्यार्थिओं की एक कक्षा में 39 लड़कियां हैं। इन लड़कियों का औसत वजन 60 किलो है और पूरी कक्षा का औसत वजन 64 किलोग्राम है। कक्षा के लड़कों का औसत वजन क्या है।

  1. 69 kg/किग्रा

  2. 66 kg/किग्रा

  3. 68 kg/किग्रा

  4. 70 kg/किग्रा
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total weight = 65×64 = 4160 kg. Girls weight = 39×60 = 2340 kg. Boys weight = 4160-2340 = 1820 kg. Number of boys = 65-39 = 26. Average boy weight = 1820/26 = 70 kg. Weighted average principle.

Multiple choice

In a class there are 41 students, whose average age is 16 years. What will be the average age of the class after three months when two students of age 17 years and 19 years exclude the class and a student of age 20 years joins the class?

  1. Less than 16 years

  2. 16 years

  3. More than 16 years and less than 20 years

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

Initial total age = 41 × 16 = 656. After 3 months, if no one left/joined: (656 + 41×3)/41 = 17 years. But two students leave (17+19 = 36) and one joins (20), so net change = -16. New total = 656 + 123 - 16 = 763. New avg = 763/40 = 19.075 years, which is between 16 and 20.

Multiple choice

The average of the test scores of a class of ‘m’ students is 70 and that of ‘n’ students is 91. When the scores of both the classes are combined, the average is 80. What is n/m? 'm' छात्रों के एक कक्षा के परीक्षा के स्कोर का औसत 70 है और ‘n’ छात्रों के कक्षा का औसत 91 है । जब दोनों वर्गों के स्कोर संयुक्त किये जाते हैं तो औसत 80 है । n/m क्या है?

  1. 10/13

  2. 10/11

  3. 11/10

  4. 13/10
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total marks = 70m + 91n. Combined average: (70m + 91n)/(m+n) = 80. Solving: 70m + 91n = 80m + 80n. This gives 11n = 10m, so n/m = 10/11. This uses the weighted average formula where overall average lies between individual averages.

Multiple choice

Average age of a class having 36 students is 16 years and 6 months. When certain number of new students entered in class having average age of 19 years 3 months, new average age of class becomes 17 years and 9 months. Find the total number of students who entered in class.

  1. 24

  2. 20

  3. 32

  4. 33

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

Let original students = 36, avg age = 16.5 years. Let x = new students, avg age = 19.25 years. New avg = 17.75 years. Total age equation: 36 x 16.5 + x x 19.25 = (36+x) x 17.75. 594 + 19.25x = 639 + 17.75x. 1.5x = 45. x = 30. Since 30 is not among options A-D (24, 20, 32, 33), answer is E (None of these).

Multiple choice

There are 20 balls, some of them are golden and the others are yellow. The average cost of all balls is Rs. 38, average cost of golden balls is Rs. 35 and that of yellow balls is Rs. 40, find the number of yellow balls.

  1. 15

  2. 18

  3. 12

  4. 16
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let yellow balls = y, golden balls = 20 - y. Total cost = 20 × 38 = 760. Golden cost: 35(20 - y), Yellow cost: 40y. Total: 35(20 - y) + 40y = 760. Solving: 700 - 35y + 40y = 760, 5y = 60, y = 12. Using allegation method: (40 - 38):(38 - 35) = 2:3, so yellow:golden = 2:3, giving yellow = 2/5 × 20 = 12.