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 are five boxes in a truck. The weight of the first box is 300 kg and the weight of the second box is 20% higher than the weight of the third box, whose weight is 25% higher than the first box’s weight. The fourth box at 400 kg is 20% lighter than the fifth box. Find the difference in the average weight of the four heaviest boxes and the four lightest boxes.

  1. 60

  2. 50

  3. 80

  4. 90
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Box 1 = 300 kg. Box 3 = 300 × 1.25 = 375 kg. Box 2 = 375 × 1.2 = 450 kg. Box 4 = 400 kg, which is 20% lighter than Box 5, so 400 = 0.8 × Box 5, giving Box 5 = 500 kg. Sorted: 300, 375, 400, 450, 500. Average of 4 lightest = (300+375+400+450)/4 = 381.25 kg. Average of 4 heaviest = (375+400+450+500)/4 = 431.25 kg. Difference = 50 kg. Option A gives 60. Option C gives 80. Option D gives 90.

Multiple choice

If we consider four numbers, the average of first three is 18 and that of last three is 19. If the last number is 16, find the first number?

  1. 13

  2. 15

  3. 11

  4. 14
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let numbers be a, b, c, d (with d = 16). Average of first three = (a+b+c)/3 = 18, so a+b+c = 54. Average of last three = (b+c+d)/3 = 19, so b+c+d = 57. Then (b+c+16) = 57, giving b+c = 41. Substituting: a + 41 = 54, so a = 13. Option B would give average of first three = 19. Option C would give average of first three = 17. Option D would give average of first three = 17.67.

Multiple choice

In a class of 178 students there are 68 girls. The average weight of these girls is 51 kg and the average weight of the whole class is 55.2 kg. What is the average weight of the boys of the class?
  1. $57.8$
  2. $56.2$
  3. $59.5$
  4. $60$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total class weight = 178 × 55.2 = 9825.6 kg. Girls' total weight = 68 × 51 = 3468 kg. Boys' weight = 9825.6 - 3468 = 6357.6 kg. Number of boys = 178 - 68 = 110. Average boys' weight = 6357.6 / 110 = 57.8 kg. Option A is correct.

Multiple choice

The average age of 14 girls and their teacher’s age is 16 years. If the teacher’s age is excluded the average reduces by 1. What is the teacher’s age? 14 लड़कियों और उनके शिक्षक की औसत आयु 16 वर्ष है। यदि शिक्षक की आयु को हटा दिया जाए तो औसत 2 कम हो जाता है। शिक्षक की आयु क्या है?

  1. 35 years 35 वर्ष

  2. 32 years 32 वर्ष

  3. 30 years 30 वर्ष

  4. 29 years 29 वर्ष

  5. 44 years 44 वर्ष
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total age of 15 people = 15 × 16 = 240 years. Without teacher, average = 15, so 14 girls' total age = 14 × 15 = 210 years. Teacher's age = 240 - 210 = 30 years. Option C is correct.

Multiple choice

The number of students in a class is 45, out of which 33.33 % are boys and the rest are girls. The average score of girls in Science in 66.66 % more than that of boys. If the average score of all the students is 78, then the average score of girls is: एक कक्षा में छात्रों की संख्या 45 है, जिसमें से 33.33% लड़के हैं और शेष लड़कियां हैं। विज्ञान में लड़कियों का औसत अंक लड़कों की तुलना में 66.66% अधिक है। यदि सभी विद्यार्थियों का औसत अंक 78 है, तो लड़कियों का औसत अंक है:

  1. 78

  2. 54

  3. 90

  4. 65

  5. 85
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

33.33% of 45 = 15 boys, 30 girls. Let boys' average = x, girls' average = x + 66.66% of x = 1.666x. Total: 15x + 30(1.666x) = 45×78 = 3510. 15x + 50x = 3510, 65x = 3510, x = 54. Girls' average = 1.666×54 = 90.

Multiple choice

The average marks of 28 students in an examination was 63. It was later found that the marks of two students had been wrongly entered as 72 and 54 instead of 52 and 46 . The correct average is:
  1. $62$
  2. $57$
  3. $64$
  4. $72$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Original total = 28 × 63 = 1764. The wrong entries were 72 and 54 (sum = 126). Correct entries are 52 and 46 (sum = 98). The total should decrease by 126 - 98 = 28. Correct total = 1764 - 28 = 1736. Correct average = 1736/28 = 62.

Multiple choice

The average marks of 45 students in the class is 86. The average marks of first 22 students is 92 and that of last 22 students is 81. Find the marks of the 23rd student in the class.

  1. 77

  2. 64

  3. 72

  4. 83
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total marks for 45 students = 45 × 86 = 3870. First 22 students total = 22 × 92 = 2024. Last 22 students total = 22 × 81 = 1782. The 23rd student's marks = Total - (First 22 + Last 22) = 3870 - (2024 + 1782) = 3870 - 3806 = 64. Option B is correct.

Multiple choice

What is the average age of the family? Statements: 1. There are 5 members in the family. 2. Sum of their ages is equal to 100.

  1. Statement 1 alone is sufficient

  2. Neither statement 1 nor 2 is sufficient

  3. Statement 1 and 2 together are sufficient

  4. Statement 2 alone is sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Statement 1 gives the count (5 members) and Statement 2 gives the sum (100). To find the average, we need both values: average = sum ÷ count. Neither statement alone is sufficient, but together they give us all the information needed.

Multiple choice

The average weight of the students in four sections A, B, C and D is 60 kg. The average weight of the students of sections A, B, C and D individually are 45 kg, 50 kg, 72 kg and 80 kg, respectively. If the average weight of the students of section A and B together is 48 kg and that of B and C together is 60 kg, what is the ratio of the number of students in sections A and D? चार वर्गों A, B, C और D में छात्रों का औसत वजन 60 किलो है। व्यक्तिगत रूप से वर्ग A, B, C और D के छात्रों का औसत वजन क्रमशः 45 किग्रा, 50 किग्रा, 72 किग्रा और 80 किग्रा है। यदि सेक्शन A और B के छात्रों का मिलाकर औसत वजन 48 किग्रा है और B और C का मिलाकर औसत वजन 60 किग्रा है, तो सेक्शन A और D में छात्रों की संख्या का अनुपात क्या है?

  1. 4:3

  2. 5:3

  3. 3 :2

  4. 6:7

  5. 5:9
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let students in A, B, C, D be a, b, c, d. Overall average 60 kg means total weight = 60(a+b+c+d). Using individual averages: 45a + 50b + 72c + 80d = 60(a+b+c+d). A+B average 48: 45a + 50b = 48(a+b), giving b = 3a. B+C average 60: 50b + 72c = 60(b+c), giving c = 5b/3 = 5a. Substituting in main equation: a + 3a + 5a + d gives ratio a:d = 4:3. A is correct.

Multiple choice

There are 35 students in a class. Number of girls in the class is 5 more than the boys. The average weight of girls is 2 kg more than the boys’ average. Total weight of girls is 190 kg more than that of boys. Calculate the average weight of the class एक कक्षा में 35 विद्यार्थी हैं। कक्षा में लड़कियों की संख्या लड़कों से 5 अधिक है। लड़कियों का औसत वजन लड़कों के औसत वजन से 2 किलो अधिक है। लड़कियों का कुल वजन लड़कों की तुलना में 190 किलो अधिक है। कक्षा के औसत वजन की गणना करें

  1. 35.56

  2. 31.14

  3. 30.89

  4. 36.16

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

Let boys = b, then girls = b + 5. Total: b + b + 5 = 35, so 2b = 30, b = 15. Boys = 15, girls = 20. Let boys' average = a, then girls' average = a + 2. Total weight: 15a = 20(a + 2) - 190, giving 15a = 20a + 40 - 190, so -5a = -150, a = 30. Boys' avg = 30, girls' avg = 32. Class average = (15×30 + 20×32)/35 = (450 + 640)/35 = 1090/35 = 31.14. Set up simultaneous equations carefully.