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

In shewak's opinion, his weight is greater than 76 kg but loss than 83 kg. His sister does not agree with shewak and she thinks that shewak's weight is greater than 71 kg but less than 81 kg. His father's view is that his weight cannot be greater than 79 kg. If all are them are correct in their estimation, what is the average of different probable weights of shewak?

  1. 67kg

  2. 68kg

  3. 72kg

  4. 78kg

  5. None
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The three estimates together give weights greater than 76 kg and at most 79 kg. Assuming weights are measured in whole kilograms, the possible values are 77, 78, and 79, whose average is 78 kg.

Multiple choice

The sum of the ages of 75 girls of a class is 1050 years. Out of these, the average age of 25 girls is 12 years and the average age of other 25 girls is 16 years. The average age of the remaining girls is:

  1. 12 years

  2. 13 years

  3. 14 years

  4. 15 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total sum = 1050. Sum of 25 girls = 25 * 12 = 300. Sum of next 25 girls = 25 * 16 = 400. Remaining girls = 75 - 25 - 25 = 25. Sum of remaining = 1050 - 300 - 400 = 350. Average = 350 / 25 = 14.

Multiple choice

There are five boxes in a box hold. The weight of the first box is 40 kg and the weight of the second box is 50% higher than the weight of the third box, whose weight is 25% higher than the first boxes' weight. The fourth box at 150 kg is 50% heavier than the fifth box. Find the difference in the average weight of the four heaviest boxes and the four lightest boxes.

  1. 21.5 kg

  2. 25 kg

  3. 27.5 kg

  4. 22.5 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Box 1 = 40. Box 3 = 40 * 1.25 = 50. Box 2 = 50 * 1.5 = 75. Box 4 = 150. Box 5 = 150 / 1.5 = 100. Weights: 40, 50, 75, 100, 150. Four heaviest: 50, 75, 100, 150 (Avg = 375/4 = 93.75). Four lightest: 40, 50, 75, 100 (Avg = 265/4 = 66.25). Difference = 93.75 - 66.25 = 27.5.

Multiple choice

The average of 60 students' results is 38. If the average of the first 22 students is 36 and that of the last 32 students is 32, then the average result of the remaining students is:

  1. 77.33

  2. 65.30

  3. 81.9

  4. 52.12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total sum = 60 * 38 = 2280. Sum of first 22 = 22 * 36 = 792. Sum of last 32 = 32 * 32 = 1024. Remaining students = 60 - 22 - 32 = 6. Sum of remaining = 2280 - 792 - 1024 = 464. Average = 464 / 6 = 77.33.

Multiple choice

The average score of 42 students in a test is 69. The ratio of the number of boys to that of girls is 10 : 11. The average score of the boys is 20% more than that of the girls. The average score of the boys is:

  1. 75.2

  2. 73.5

  3. 75.6

  4. 82.8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

With a 10:11 ratio of boys to girls among 42 students, there are 20 boys and 22 girls. Let the average score of the girls be g, making the boys' average score 1.2g. The total score of the class is 20 * 1.2g + 22 * g = 46g, which must equal 42 * 69 = 2,898, solving to g = 63. Thus, the average score of the boys is 1.2 * 63 = 75.6.

Multiple choice

The total number of students in sections A and B of a class is 72. The ratio of the number of students in A and B is 7 : 5. The average weight (in kg) of the students in section B is 20% more than that of the students in section A. If the average weight of all the students in the class is 52 kg, then what is the average weight (in kg) of the students in section B?

  1. 58.2

  2. 57.9

  3. 57.6

  4. 56.4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ratio A:B = 7:5. Students in A = 42, B = 30. Let avg weight of A = x, then B = 1.2x. Total weight = 42x + 30(1.2x) = 72 * 52. 42x + 36x = 3744. 78x = 3744, x = 48. Avg weight of B = 1.2 * 48 = 57.6.

Multiple choice

The average of ten numbers is 72. The average of the first four numbers is 69 and that of the next three numbers is 74. The 8th number is 6 more than the 9th number and 12 more than the 10th number. What is the average of the 8th and 9th numbers?

  1. 76

  2. 76.5

  3. 77.5

  4. 77
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total sum = 10 * 72 = 720. Sum of first 4 = 4 * 69 = 276. Sum of next 3 = 3 * 74 = 222. Sum of last 3 = 720 - 276 - 222 = 222. Let 10th number be x. 8th = x+12, 9th = x+6. (x+12) + (x+6) + x = 222 => 3x + 18 = 222 => 3x = 204 => x = 68. 8th = 80, 9th = 74. Average = (80+74)/2 = 77.

Multiple choice

In a classroom, the ratio of the number of girls to that of boys is 3 : 4. The average height of students in the class is 4.6 feet. If the average height of the boys in the class is 4.8 feet, then what is the average height of the girls in the class?

  1. Less than 4.2 feet

  2. More than 4.2 feet but less than 4.3 feet

  3. More than 4.3 feet but less than 4.4 feet

  4. More than 4.4 feet but less than 4.5 feet
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the number of girls be 3k and boys be 4k. Total students = 7k. Total height = 7k * 4.6 = 32.2k. Total height of boys = 4k * 4.8 = 19.2k. Total height of girls = 32.2k - 19.2k = 13k. Average height of girls = 13k / 3k = 4.33 feet.

Multiple choice

Directions: The following question consists of two quantities, Quantity I and Quantity II. You are to compare the two quantities and find the correct relationship between both the quantities. Quantity I: The distance traveled by Rajesh in 61 hrs at the average speed for the entire trip if Rajesh rides his bike 20 km at average speed of 24 kmph and again travels 24 km at average speed of 20 kmph. Quantity II: The distance traveled by Pawan in 40 hrs at the average speed for the entire trip if Pawan covers a distance of 25 km at average speed of 30 kmph by his car and again travels 40 km at average speed of 25 kmph.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≤ Quantity II

  4. Quantity I ≥ Quantity II

  5. Quantity I = Quantity II or No relation
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: Avg speed = Total Distance / Total Time. Time 1 = 20/24 = 5/6 hr. Time 2 = 24/20 = 6/5 hr. Total time = 5/6 + 6/5 = 61/30 hr. Total distance = 44 km. Avg speed = 44 / (61/30) = 1320/61 kmph. Distance in 61 hrs = (1320/61) * 61 = 1320 km. Quantity II: Time 1 = 25/30 = 5/6 hr. Time 2 = 40/25 = 8/5 hr. Total time = 5/6 + 8/5 = 73/30 hr. Total distance = 65 km. Avg speed = 65 / (73/30) = 1950/73 kmph. Distance in 40 hrs = (1950/73) * 40 = 78000/73 = 1068.49 km. Quantity I > Quantity II.

Multiple choice

Directions: In the following item, quantity I and quantity II are given. Determine the relationship between the quantities and choose the appropriate option. Quantity I: The average mark of the class when in a class of 60 students, 23 are girls, the average mark of boys is 45, and the average mark of girls is 52 Quantity II: The average mark of the class when in a class of 40 students, 15 are boys, the average mark of boys is 60, and the average mark of girls is 40

  1. Quantity I < Quantity II

  2. Quantity I > Quantity II

  3. Quantity I ≤ Quantity II

  4. Quantity I ≥ Quantity II

  5. Quantity I = Quantity II or the relationship cannot be established from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I: (23*52 + 37*45)/60 = (1196 + 1665)/60 = 2861/60 = 47.68. Quantity II: (25*40 + 15*60)/40 = (1000 + 900)/40 = 1900/40 = 47.5. Since 47.68 > 47.5, Quantity I > Quantity II.