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

Four numbers are written in a row. The average of the first two numbers is 7, the average of the middle two terms is 2.3 and the average of the last two numbers is 8.4. The average of the first number and the last number is:

  1. 5.9

  2. 10.7

  3. 13.1

  4. Cannot be determined

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

Let numbers be a, b, c, d. (a+b)/2 = 7 -> a+b = 14. (b+c)/2 = 2.3 -> b+c = 4.6. (c+d)/2 = 8.4 -> c+d = 16.8. We need (a+d)/2. From equations: a+d = (a+b) + (c+d) - (b+c) = 14 + 16.8 - 4.6 = 26.2. Average = 26.2 / 2 = 13.1.

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?

  1. 69 kg

  2. 66 kg

  3. 68 kg

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

Total weight of class = 65 * 64 = 4160. Total weight of girls = 39 * 60 = 2340. Total weight of boys = 4160 - 2340 = 1820. Number of boys = 65 - 39 = 26. Average weight of boys = 1820 / 26 = 70 kg.

Multiple choice

In a class there are 32 boys and 28 girls. The average age of the boys in the class is 14 years, and the average age of the girls in the class is 13 years. What is the average age of the whole class? (Rounded off to two digits after decimal)

  1. 13.50 years

  2. 13.53 years

  3. 12.51 years

  4. 13.42 years

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

Total age = (32 * 14) + (28 * 13) = 448 + 364 = 812. Total students = 32 + 28 = 60. Average = 812 / 60 = 13.5333.

Multiple choice

The average of two observations, a and 12, will become c, when both the observations are doubled and one is added to each observation. The average of two observations, 5a and 16, will become d, when both the observations are doubled and one is added to each observation. What is the average of c and d?

  1. 3a + 5

  2. 3a + 10

  3. 3a + 15

  4. 3a + 20

  5. 3a + 25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The average of a and 12 is (a+12)/2. Doubling and adding 1 gives (2a+1) and (25), so c = (2a+1+25)/2 = a+13. For 5a and 16, doubling and adding 1 gives (10a+1) and (33), so d = (10a+1+33)/2 = 5a+17. The average of c and d is (a+13+5a+17)/2 = (6a+30)/2 = 3a+15.

Multiple choice

A speaker talked for sixty minutes to a full auditorium. Ten percent of the audience listened to the entire talk, and twenty percent slept through the entire talk. Half of the remaining listened to one-third of the talk, and the other half listened to two-thirds of the talk. Find out the average number of minutes for which the audience listened to the talk.

  1. 25

  2. 26

  3. 27

  4. 31
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

10% listened for 60 min. 20% listened for 0 min. Remaining 70%: half (35%) listened for 1/3 of 60 = 20 min, half (35%) listened for 2/3 of 60 = 40 min. Average = (0.1*60 + 0.2*0 + 0.35*20 + 0.35*40) = 6 + 0 + 7 + 14 = 27.

Multiple choice

The average weight of 50 players is 60 kg. If the players with weights 60 kg and 65 kg leave and three new players join, then the average remains unchanged. Find the average weight of three players who joined later.

  1. 73.37 kg

  2. 85 kg

  3. 61.67 kg

  4. 65.5 kg

  5. 70 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial sum = 50 * 60 = 3000. After two leave, sum = 3000 - 60 - 65 = 2875. With 3 new players, total players = 51. Since average remains 60, new sum = 51 * 60 = 3060. Sum of 3 new players = 3060 - 2875 = 185. Average = 185 / 3 = 61.666...

Multiple choice

Four persons A, B, C and D were checking their weights on a weighing machine. A's weight was 70 kg. C's weight was 30% less than D's weight. D's weight was 30 kg less than that of B. If the ratio of B's weight to that of C is 16 : 7, the average weight of A, B and C is

  1. 59.33 kg

  2. 61.36 kg

  3. 61.66 kg

  4. 62.33 kg

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

A = 70. D = B - 30. C = 0.7D = 0.7(B - 30). Ratio B/C = 16/7 implies B / (0.7(B - 30)) = 16/7. Solving for B: 7B = 11.2(B - 30) => 7B = 11.2B - 336 => 4.2B = 336 => B = 80. Then D = 50, C = 35. Average of A, B, C = (70 + 80 + 35) / 3 = 185 / 3 = 61.66.

Multiple choice

When two students of a class of 40 students were expelled, the average age of the class, which was 18 years, did not change. If one of the students was 14 years old, what was the age (in years) of the second student?

  1. 22

  2. 24

  3. 26

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

Total age = 40 * 18 = 720. After 2 students leave, 38 students remain with average 18. New total = 38 * 18 = 684. Sum of removed students = 720 - 684 = 36. If one is 14, the other is 36 - 14 = 22.