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 group of boys has an average weight of 36 kg. One boy weighing 42 kg leaves the group and another boy weighing 30 kg joins the group. If the average now becomes 35.7 kg, then how many boys are there in the group?

  1. 30

  2. 32

  3. 40

  4. 56

  5. 60
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let n be the number of boys. Total weight = 36n. New total weight = 36n - 42 + 30 = 36n - 12. New average = (36n - 12) / n = 35.7. 36n - 12 = 35.7n. 0.3n = 12. n = 12 / 0.3 = 40.

Multiple choice

The average age of students in a class is 25 years. If the oldest and the youngest students are excluded, then the average is equal to 2 more than the average age of the youngest and the oldest. The oldest student is 28 years and is 8 years older than the youngest. What is the number of students in the class?

  1. 2

  2. 4

  3. 6

  4. 8

  5. 10
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let n be the number of students and S be the sum of their ages. S/n = 25, so S = 25n. The oldest is 28, and the youngest is 28 - 8 = 20. Excluding them, the sum is 25n - 48, and the number of students is n - 2. The new average is (25n - 48)/(n - 2) = ((28 + 20)/2) + 2 = 26. Solving 25n - 48 = 26n - 52 gives n = 4.

Multiple choice

A person goes from point N to P and comes back. His average speed for the whole journey is 60 km/hr. If his speed while going from N to P is 40 km/hr, then what will be the speed of the person (in km/hr) while coming back from P to N?

  1. 80

  2. 100

  3. 120

  4. 140
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average speed = 2xy / (x+y), where x and y are the speeds for the two legs. 60 = 2 * 40 * y / (40 + y). 60(40 + y) = 80y. 2400 + 60y = 80y. 20y = 2400, so y = 120.

Multiple choice

The average age of 150 people watching a movie in a theatre is 23.7 years. If the age of 2 persons has been mistakenly written as 72 and 43 instead of 27 and 33, then what is the actual average age of the group of people?

  1. 23.22 years

  2. 23.33 years

  3. 24.15 years

  4. 24.45 years

  5. 24.76 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The total sum of ages is 150 * 23.7 = 3555. The error was adding 72 and 43 (115) instead of 27 and 33 (60), meaning the sum was overstated by 55. The corrected sum is 3555 - 55 = 3500, and the new average is 3500 / 150 = 23.33.

Multiple choice

The average marks obtained by 180 students in an examination are 50. If the average marks obtained by students who have passed are 80 and that obtained by students who have failed are 40, then what is the number of students who have failed the examination?

  1. 90

  2. 135

  3. 100

  4. 45
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let F be the number of failed students and P be the number of passed students. P + F = 180. Total marks = 180 * 50 = 9000. 80P + 40F = 9000. Substitute P = 180 - F: 80(180 - F) + 40F = 9000 => 14400 - 40F = 9000 => 40F = 5400 => F = 135.