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 weight of 33 students in a class is 45 kg. If the weight of the teacher and a new student is to be included then the average of the whole class increases by 1 kg. Then what was the average weight of the teacher and the new student ?

  1. 55 kg

  2. 60 kg

  3. 72 kg

  4. 62.5 kg

  5. 56 kg
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial sum = 33 * 45 = 1485. New sum = 35 * 46 = 1610. Sum of the two new people = 1610 - 1485 = 125. Average = 125 / 2 = 62.5 kg.

Multiple choice

In a Science fair competition, there are 50 participants consisting of students and teachers. The average score of the students is 75 points, while the average score of the teachers is 85 points. If the overall average score of the participants is 78 points, what is the ratio of the number of students to the number of teachers in the competition?

  1. 4 : 7

  2. 3 : 4

  3. 7 : 3

  4. 4 : 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let S be the number of students and T be the number of teachers. Using the weighted average formula: (75S + 85T) / (S + T) = 78. This simplifies to 75S + 85T = 78S + 78T, or 7T = 3S, so S/T = 7/3.

Multiple choice

Directions: The problem contains a question and two statements giving certain data. You have to select the correct answer from the given options depending on the sufficiency of the data given in the statements to answer the question. What is the total number of employees in the XYZ company? (A) The average monthly salary of each employee is \$5000. (B) The total monthly salary of the all employees in the XYZ company is \$200,000.

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

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

  3. Both statements together are sufficient.

  4. Each statement alone is sufficient.

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

Let N be the number of employees. Total salary = Average salary * N. Statement A gives Average = 5000. Statement B gives Total = 200,000. Using both, 200,000 = 5000 * N, so N = 40. Neither alone is sufficient.

Multiple choice

A company has 60 employees whose names are listed in a certain order. In the year 2022, the average salary of the first 40 employees was Rs. 35,000, of the last 40 employees was Rs. 50,000, and of the first 20 and last 20 employees combined was Rs. 45,000. In 2023, the average salary of the first 20 employees increased by 20%, of the last 20 employees increased by 30%, and of the remaining employees remained unchanged. What was the average salary, in rupees, of all 60 employees together in 2023?

  1. Rs. 50,000

  2. Rs. 51,333

  3. Rs. 52,672

  4. Rs. 53,647
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

The average weight of 52 boys in a class was estimated to be 38 kg, whereas the total weight of 48 girls in the same class was estimated to be 1728 kg. If with the addition of 10 new students to the class, the average weight for the class changed to 38 kg, what was the average weight of the 10 new students?

  1. 47.6 kg

  2. 48.6 kg

  3. 49.6 kg

  4. 50.6 kg

  5. 51.6 kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total weight of 52 boys = 52 * 38 = 1976. Total weight of 48 girls = 1728. Total weight of 100 students = 1976 + 1728 = 3704. New total students = 110. New average = 38. New total weight = 110 * 38 = 4180. Weight of 10 new students = 4180 - 3704 = 476. Average = 476 / 10 = 47.6 kg.

Multiple choice

The average of marks for a class in science is 64 and the total number of students is 30. If the average of marks for girls is 78, and the number of boys is 18, what is the approximate average of marks scored by the boys?

  1. 55

  2. 60

  3. 64

  4. 72

  5. 74
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total students = 30. Girls = 30 - 18 = 12. Total marks = 30 * 64 = 1920. Girls' total = 12 * 78 = 936. Boys' total = 1920 - 936 = 984. Boys' average = 984 / 18 = 54.66, which is approximately 55.

Multiple choice

What is the minimum rating that the 16th customer of the shop gives to a new product launched by the company at the store,if the feedback ratings from 15 customers on a scale of 20 to 120 has an average rating of 78, and overall average rating from 16 customers for the product is at least 80?

  1. 70

  2. 80

  3. 110

  4. 120
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total sum for 15 customers = 15 * 78 = 1170. Total sum for 16 customers = 16 * 80 = 1280. The 16th customer must contribute 1280 - 1170 = 110.

Multiple choice

Sarah sold 12 art pieces at her gallery last month. During the first week of the month, she sold the first 5 pieces at \$700 each. As demand increased later in the month, she raised the price of the remaining 7 pieces by \$60 per piece. What was the average selling price of the 12 art pieces sold last month?
  1. $715
  2. $720
  3. $735
  4. $745
  5. $755
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total revenue = (5 * 700) + (7 * (700 + 60)) = 3500 + 5320 = 8820. Average = 8820 / 12 = 735.

Multiple choice

In a classroom, the average score of five students in a test is 70. If the highest score among them is added to their total score, the new average becomes 75. What is the score of the student with the highest score?

  1. 95

  2. 100

  3. 105

  4. 110
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial total score for 5 students is 5 * 70 = 350. With the highest score added, there are now 6 scores (or the total sum increases), but the problem implies the new average is for the original 5 students plus the highest score, making 6 items. Total sum = 6 * 75 = 450. The highest score is 450 - 350 = 100.