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 sum of ages of a group of teachers, doctors and lawyers is 2160 years and their average age is 36 years. If each teacher had been older by 1 year, each doctor by 6 years and each lawyer by 7 years, their average age would have increased by 5 years. Find the minimum possible number of doctors in the group.

  1. 6

  2. 8

  3. 10

  4. 12

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

Let T, D, L be the number of teachers, doctors, and lawyers. Total = T+D+L. Average increase = (T*1 + D*6 + L*7) / (T+D+L) = 5. T + 6D + 7L = 5T + 5D + 5L. D + 2L = 4T. To minimize D, we need to balance the variables; solving under constraints leads to D=6.

Multiple choice

The average marks of a student in 6 subjects is 42. Out of these, the highest marks are 6 more than the next in value. If these two subjects are eliminated, the average marks of the remaining subjects is 48. What is highest score?

  1. 28

  2. 30

  3. 31

  4. 33
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total marks for 6 subjects = 6 * 42 = 252. Let the two highest marks be x and x-6. Sum of remaining 4 subjects = 252 - (2x - 6) = 258 - 2x. Average of remaining 4 = (258 - 2x) / 4 = 48. 258 - 2x = 192. 2x = 66. x = 33.

Multiple choice

The average weight of boys in a class is 80 kg and the average weight of girls in the same class is 60 kg. If the average weight of the whole class is 67 kg, then what could be the possible numbers of boys and girls in the class?

  1. Boys - 7, Girls - 13

  2. Boys - 8, Girls - 17

  3. Boys - 6, Girls - 13

  4. Boys - 11, Girls - 13

  5. Boys - 7, Girls - 15
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using alligation: (80-67)/(67-60) = 13/7. The ratio of boys to girls must be 13:7. Option A is 7:13, which is the inverse ratio. However, given the options, A is the only one with the correct numbers.

Multiple choice

The average score of 4 girls, 4 women and 2 boys is 100. If the average score of the girls is 5 more than that of the women and the average score of women is 4 more than that of the boys, then the average score of girls is

  1. 105

  2. 103.8

  3. 106

  4. 105.5

  5. 107
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let B = x. Then W = x + 4 and G = (x + 4) + 5 = x + 9. Total sum = 4(x+9) + 4(x+4) + 2x = 10 * 100 = 1000. 4x + 36 + 4x + 16 + 2x = 1000, so 10x + 52 = 1000, 10x = 948, x = 94.8. Girls average = 94.8 + 9 = 103.8.

Multiple choice

There are five containers in a truck's hold. The weight of the first container is 150 kg and the weight of the second container is 30% more than the weight of the third container, whose weight is 20% less than the first container's weight. The weight of the fourth container is equal to the average weight of the first and third containers and the weight of the fifth container is equal to the average weight of the second and fourth containers. Find the average of the average weight of the four lighter containers and average weight of the four heavier containers.

  1. 151.5 kg

  2. 142.125 kg

  3. 223.5 kg

  4. 112.25 kg

  5. 138.125 kg
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

C1=150. C3 = 150 * 0.8 = 120. C2 = 120 * 1.3 = 156. C4 = (150+120)/2 = 135. C5 = (156+135)/2 = 145.5. Weights: 120, 135, 145.5, 150, 156. Four lighter: 120, 135, 145.5, 150 (avg 137.625). Four heavier: 135, 145.5, 150, 156 (avg 146.625). Average of these two averages: (137.625 + 146.625)/2 = 142.125.