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 classroom has a total of 120 students. They appear in an examination and get an average of 65 marks. The students who have passed the examination have an average of 74 marks, while the failed students have an average of 20 marks. The number of failed students is

  1. 20

  2. 16

  3. 18

  4. 14

  5. 22
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x be the number of failed students. Then 120-x is the number of passed students. Total marks = 120 * 65 = 7800. Passed marks = (120-x) * 74. Failed marks = x * 20. (120-x)*74 + 20x = 7800. 8880 - 74x + 20x = 7800. 54x = 1080. x = 20.

Multiple choice

Directions: This data sufficiency problem consists of a question and two statements labelled (1) and (2). You have to decide whether the data given in the statements is sufficient for answering the question. What was Riya's score on the fourth physics test she took? (1) Her score on the fourth test was 12 points higher than her average (arithmetic mean) score on the first three tests she took. (2) Her score on the fourth test raised her average (arithmetic mean) test score from 87 to 90.

  1. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

  3. Both statements (1) and (2) together are sufficient, but none of them alone is sufficient.

  4. Each statement alone is sufficient.

  5. Statements (1) and (2) together are not sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Statement (1) only gives a relationship between the fourth test score and the average of the first three tests, which is insufficient to find the exact score. Statement (2) provides the average of the first three tests (87) and the average of all four tests (90), allowing us to calculate the total score of the first three tests (261) and the total score of all four tests (360). The difference, 360 - 261 = 99, is the score of the fourth test, making Statement (2) alone sufficient.

Multiple choice

The average weight of men 'X', 'Y' and 'Z' is 75 kg. Another man 'A' joins the group and the average weight now becomes 80 kg. If another person 'B', whose weight is 5 kg more than 'A', replaces 'X', then the average weight of 'Y', 'Z', 'A' and 'B' will be 85 kg. What is the weight of 'X'?

  1. 80 kg

  2. 84 kg

  3. 82 kg

  4. 78 kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

X+Y+Z = 225. X+Y+Z+A = 320 -> A = 95. B = A + 5 = 100. Y+Z+A+B = 85 * 4 = 340. Y+Z+95+100 = 340 -> Y+Z = 145. X = 225 - (Y+Z) = 225 - 145 = 80.

Multiple choice

The average age of 15 boys in a class is 19 years and average age of 20 girls is 17 years. Then find out the combined average age of all the students of the class.

  1. 17.36 Years

  2. 18 Years

  3. 17.86 Years

  4. 17.50 Years

  5. 19 Years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The combined average is calculated by finding the total sum of ages and dividing by the total number of students. Total sum = (15 * 19) + (20 * 17) = 285 + 340 = 625. Combined average = 625 / 35 = 17.857, which rounds to 17.86.

Multiple choice

In a cricket team, the average age of 11 players is 22 years. If the age of their coach is also to be included in this average age, then the new average age would be 23 years. What is the age of their coach?

  1. 34 years

  2. 23 years

  3. 22 years

  4. 22.5 years

  5. 43 years
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total age of 11 players is 11 * 22 = 242. Including the coach, there are 12 people with an average age of 23, so the new total is 12 * 23 = 276. The coach's age is 276 - 242 = 34.

Multiple choice

In a park there are 120 marbles in which red, blue and green marbles are in the ratio 5 : 4 : 3. The average weight of the blue marbles is 30 grams, that of the red marbles is 60 grams and that of the green marbles is half that of the blue marbles. Find the mean weight of all the marbles.

  1. 38.75 grams

  2. 39.75 grams

  3. 40.75 grams

  4. 41.75 grams

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

Total marbles = 120. Ratio 5:4:3 means 50 red, 40 blue, 30 green. Weights: Blue = 30g, Red = 60g, Green = 15g (half of blue). Total weight = (50 * 60) + (40 * 30) + (30 * 15) = 3000 + 1200 + 450 = 4650. Mean weight = 4650 / 120 = 38.75g.

Multiple choice

The average weight of Shubha, Govinda and Reshma is 65 kg. If the average weight of Shubha and Govinda be 63 kg and that of Govinda and Reshma be 70 kg, then the weight of Govinda is

  1. 41 kg

  2. 71 kg

  3. 88 kg

  4. 46 kg
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sum of weights of S, G, R = 65 * 3 = 195. Sum of S and G = 63 * 2 = 126. Sum of G and R = 70 * 2 = 140. Adding (S+G) and (G+R) gives S + 2G + R = 266. Subtracting (S+G+R) from this gives G = 266 - 195 = 71.

Multiple choice

There are 5 consecutive numbers in a list and their average is 23. If the next 5 consecutive numbers are also included in the list, what will be the average of all the ten numbers?

  1. 24

  2. 24.5

  3. 25.5

  4. 25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average of 5 consecutive numbers is the middle number. If the average is 23, the numbers are 21, 22, 23, 24, 25. The next 5 are 26, 27, 28, 29, 30. The average of all 10 is (21+22+23+24+25+26+27+28+29+30)/10 = 255/10 = 25.5.

Multiple choice

The average age of 120 members of a society is 60.7 years. By addition of 30 new members, the average age becomes 56.3 years. What is the average age (in years) of newly joined members?

  1. 38.7

  2. 37.2

  3. 38.3

  4. 36.5

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

The total age of the initial 120 members is 120 * 60.7 = 7,284 years. After 30 new members join, the total age of the 150 members is 150 * 56.3 = 8,445 years. The sum of the ages of the new members is 8,445 - 7,284 = 1,161 years, which gives an average age of 1,161 / 30 = 38.7 years.