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 a batch of 19 members is 24 years. If the age of the faculty be included, then the average increases by 4 months. What is the age of the faculty?

  1. 35 years

  2. 30 years 8 months

  3. 37 years 4 months

  4. 32 years 8 months
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total age of 19 members = 19 * 24 = 456 years. New total age (20 people) = 20 * (24 years + 4 months) = 20 * 24 years + 20 * 4 months = 480 years + 80 months = 480 + 6 years + 8 months = 486 years 8 months. Faculty age = 486y 8m - 456y = 30 years 8 months.

Multiple choice

A train covers 3584 km in 2 days 8 hours. If it covers 1440 km on the first day and 1608 km on the second day, by how much does the average speed of the train for the remaining part of the journey differ from that for the entire journey?

  1. 3 km/hour more

  2. 3 km/hour less

  3. 4 km/hour more

  4. 5 km/hour less

  5. 4 km/hour less
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total distance = 3584 km, Total time = 56 hours. Average speed = 3584/56 = 64 km/h. Remaining distance = 3584 - 1440 - 1608 = 536 km. Remaining time = 56 - 24 - 24 = 8 hours. Remaining speed = 536/8 = 67 km/h. Difference = 67 - 64 = 3 km/h more.

Multiple choice

The average age of a class is 40 years. 12 new students with an average age of 32 years join the class, thereby decreasing the average age by 4 years. The original strength of the class was:

  1. 10

  2. 11

  3. 12

  4. 13

  5. 14
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the original number of students. The total age is 40x. After 12 students join, the total age is 40x + 12*32, and the new average is 40 - 4 = 36. So, (40x + 384) / (x + 12) = 36. Solving for x gives 40x + 384 = 36x + 432, which leads to 4x = 48, so x = 12.

Multiple choice

The average age of 40 student of a class is 18 yr. when 20 new students are admitted to the same class, the average age of the students of the class is increased by 6 months. The average age of newly admitted students is

  1. 19yr

  2. 19yr 6 months

  3. 20 yr

  4. 20 yr 6 months
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial sum = 40 * 18 = 720. New total students = 60. New average = 18.5. New sum = 60 * 18.5 = 1110. Sum of 20 new students = 1110 - 720 = 390. Average of new students = 390 / 20 = 19.5 years = 19 years 6 months.

Multiple choice

The average weight of 32 students of a class was 58.5kg. After 8 new students joined the class, its average weight Increased by 1.2 kg. What is the average weight of 8 new students who joined the class? (in kg)

  1. 62.5

  2. 64.5

  3. 65

  4. 63

  5. 63.5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total weight of 32 students = 32 * 58.5 = 1872. Total weight of 40 students = 40 * (58.5 + 1.2) = 40 * 59.7 = 2388. Weight of 8 new students = 2388 - 1872 = 516. Average = 516 / 8 = 64.5.

Multiple choice

There are 14 members in a yoga training centre. Four members of it leave and 6 new members join the centre. As a result, the average age of the members of the centre decreases by 5 years and the sum of all members also decreases by 20 years. What is the new average age of the members?

  1. 28 years

  2. 27 years

  3. 25 years

  4. 29 years

  5. 24 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let S be the initial sum of ages. Initial average = S/14. New sum = S - 20. New number of members = 14 - 4 + 6 = 16. New average = (S-20)/16. Given S/14 - (S-20)/16 = 5. 16S - 14(S-20) = 5 * 14 * 16 = 1120. 2S + 280 = 1120 => 2S = 840 => S = 420. New average = (420-20)/16 = 400/16 = 25.

Multiple choice

In a yoga class there were 12 members. Two members left the class and 4 new members joined. If the average age decreased by 4 years and the total age decreased by 2 years, what is the new average age of the class (In years)

  1. 22

  2. 27

  3. 26

  4. 23

  5. 18
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the initial total age be S and initial average be A = S/12. After changes, total members = 12 - 2 + 4 = 14. New total age = S - 2. New average = (S - 2) / 14 = A - 4. Substituting S = 12A, we get (12A - 2) / 14 = A - 4, leading to 12A - 2 = 14A - 56, so 2A = 54, A = 27. The new average is 27 - 4 = 23.

Multiple choice

Average weight of a class is 30 kg. 5 students more come whose age is 50 kg and 5 student leave of weight 20 kg. If total number of students in class, initially is 20 then find change percentage in average weight

  1. 10%

  2. 20%

  3. 25%

  4. 30%

  5. 40%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The initial total weight is 20 x 30 = 600 kg. Adding 5 students weighing 50 kg each and removing 5 weighing 20 kg each gives a new total of 750 kg, with 20 students still present. The average rises from 30 kg to 37.5 kg, an increase of 25%.