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

A class has 20 boys and 30 girls. The average age of boys is 11 years and that of girls is 12 years. What is the average age of the whole class?
  1. $11.6 years$
  2. $12 years$
  3. $11.2 years$
  4. $10 years$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total age of boys = 20 × 11 = 220 years. Total age of girls = 30 × 12 = 360 years. Combined total age = 580 years. Total students = 50. Average = 580 ÷ 50 = 11.6 years. This is a weighted average problem where the weights are the number of boys and girls.

Multiple choice

After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member?

  1. 2 years

  2. 4 years

  3. 8 years

  4. 10 years

  5. 15 years
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Let the sum of ages of 5 members three years ago be S. Their average age then was S/5. Three years later, each of the 4 remaining members aged 3 years, so their total increased by 12. The new member's age is such that the new sum equals S. If the replaced member was x years old and the new member is y years old, then S = (sum of 4 members' ages 3 years ago) + x = (sum of 4 members' current ages - 12) + x. Also, S = (sum of 4 members' current ages) + y. Therefore y = x - 15, meaning the new member is 15 years younger than the replaced member.

Multiple choice

The average of 35 results is 75 and the average of the first 18 of them is 78 and the average of the last 18 is 73. Then find the 18th number.

  1. 110

  2. 93

  3. 67

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

Sum of all 35 numbers = 35 × 75 = 2625. Sum of first 18 = 18 × 78 = 1404. Sum of last 18 = 18 × 73 = 1314. The 18th number is counted in both the first 18 and last 18. So: Sum(first 18) + Sum(last 18) = Total + 18th number. Therefore: 1404 + 1314 = 2625 + 18th number, giving 2718 = 2625 + 18th number, so 18th number = 2718 - 2625 = 93.

Multiple choice

In a prep school, the average weight of 30 girls in a class among 50 student is 16 kg. and that of the remaining students is 15.5 kg. What is the average weight of all the students in the class?

  1. 15.2 kg.

  2. 15.8 kg.

  3. 15.4 kg.

  4. 15.6 kg.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total weight = (30 × 16) + (20 × 15.5) = 480 + 310 = 790 kg. Average = 790/50 = 15.8 kg. This uses weighted average: (30/50 × 16) + (20/50 × 15.5) = 9.6 + 6.2 = 15.8. Options A (15.2), C (15.4), and D (15.6) are incorrect.

Multiple choice

A train traveled at a speed of 35 km./hr. for the first 10 minutes and at a speed of 20 km./hr. for the next 5 minutes. The average speed of the train for the total 15 minutes is -

  1. 30 km./hr.

  2. 23 km./hr.

  3. 31 km./hr.

  4. 29 km./hr.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total distance = 35 × (10/60) + 20 × (5/60) = 350/60 + 100/60 = 450/60 = 7.5 km. Total time = 15 minutes = 0.25 hours. Average speed = 7.5/0.25 = 30 km/hr. This equals (35×10 + 20×5)/(10+5) = 450/15 = 30.

Multiple choice

4 boys and 3 girls spent Rs. 120 on the average, of which boys spent Rs. 150 on the average. Then the average amount spent by the girls is -

  1. Rs. 80

  2. Rs. 60

  3. Rs. 90

  4. Rs. 100
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let girls' average be g. Total spent by all 7 people = 7 × 120 = 840. Boys' total = 4 × 150 = 600. Girls' total = 840 - 600 = 240. Girls' average = 240/3 = 80. This matches option A. The weighted average formula confirms: (4×150 + 3×g)/7 = 120, giving g = 80.

Multiple choice

5 members of a team are weighed consecutively and their average weight calculated after each member is weighted. If the average weight increases by one kg each time, how much heavier is the last player than the first one?

  1. 4 kg.

  2. 20 kg.

  3. 8 kg.

  4. 5 kg.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the 5 members' weights be w1, w2, w3, w4, w5. After 1st person: avg = w1. After 2nd: avg = (w1+w2)/2 = w1+1, so w2 = w1+2. After 3rd: avg = (w1+w2+w3)/3 = w1+2, so w3 = w1+4. After 4th: w4 = w1+6. After 5th: w5 = w1+8. Last player (w5) is 8 kg heavier than first (w1). Answer is correct.

Multiple choice

The marks obtained by Sulabh in Science is equal to the average marks obtained by Neetu and Shyam in Science. If Sulabh obtained 35 marks in Science and the sum of marks obtained by all the three is 145, how much marks did Neetu obtain in Science?

  1. 40

  2. 30

  3. 45

  4. Can't be determined

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

Sulabh's marks (35) equals the average of Neetu and Shyam. Let Neetu = N and Shyam = S. Then (N + S)/2 = 35, so N + S = 70. Total of all three is 145, so 35 + N + S = 145, giving N + S = 110. But we also have N + S = 70 from the first equation. This inconsistency means the problem has no valid solution, and even if we ignore it, we can only find N + S, not N individually.

Multiple choice

The questions given below contain three statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question? How many marks did Arun get in English? (A) Arun secured an average of 60 marks in four subjects including English. (B) He secured a total of 170 in English and Mathematics together. (C) He secured a total of 180 in Mathematics and Science together.

  1. All A, B and C together are required.

  2. Only A and B together are required

  3. Only B and C together are required

  4. Only A and C together are required

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

Statement A: Average of 4 subjects = 60 → total = 240. But we don't know individual subject marks. Statement B: English + Math = 170. Statement C: Math + Science = 180 → Math = 180 - Science. Combining B and C: English + (180 - Science) = 170 → English = Science - 10. But without knowing Science, we can't find English. Statement A alone or with others doesn't help because we have 4 unknowns. Therefore, English marks cannot be uniquely determined, making option E correct.

Multiple choice

A boy found that the average of 20 numbers is 35 when he writes a number 61 instead of 16. The correct average of 20 numbers is

  1. 32.75

  2. 37.25

  3. 34.75

  4. 34.25
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When 61 is written instead of 16, the sum increases by 61-16=45. The incorrect average is higher by 45/20 = 2.25. Incorrect average = 35, so correct average = 35 - 2.25 = 32.75. Alternatively: incorrect sum = 20×35=700, correct sum = 700-45=655, correct average = 655/20 = 32.75.

Multiple choice

The average of marks of 45 students in a class is 40. The average of those who pass is 52 and those who fail is 16. How many students are failed?

  1. 15

  2. 30

  3. 25

  4. Data inadequate

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

Let f be the number of students who failed and p be those who passed. We have f + p = 45. Total marks = 45 × 40 = 1800. Also: 52p + 16f = 1800. Substituting p = 45 - f: 52(45 - f) + 16f = 1800, giving 2340 - 52f + 16f = 1800, so 2340 - 36f = 1800, therefore 36f = 540 and f = 15. The marked answer (A: 15) is correct.

Multiple choice

The average of 15 numbers is 40. The average of the first eight numbers is 30. If the average of the last eight numbers is 50, then the eighth number is
  1. $40$
  2. $45$
  3. $50$
  4. $35$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Sum of 15 numbers = 15 × 40 = 600. Sum of first 8 = 8 × 30 = 240. Sum of last 8 = 8 × 50 = 400. Note: 8th number is counted in both groups. Let 8th number = x. Then 240 + 400 - x = 600, so x = 640 - 600 = 40. The 8th number is 40. Option B (45) and C (50) are incorrect. Option D (35) is also wrong.

Multiple choice

The average of 15 results is 35. The average of the first 8 results is 38, and the average of the last 8 results is 34. What is the 8th result?

  1. 53

  2. 48

  3. 51

  4. 45

  5. 57
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The sum of all 15 results is 15 × 35 = 525. The sum of the first 8 results is 8 × 38 = 304. The sum of the last 8 results is 8 × 34 = 272. Since the 8th result is counted in both groups, we have: sum(first 8) + sum(last 8) = total + 8th result. Therefore: 304 + 272 = 525 + 8th result, so 576 = 525 + 8th result, giving 8th result = 51. Option C is correct.