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 maths average arithmetic mean of ap introduction to averages means

The average age of 36 student in a group is 14 years. When teacher's age is included to it, the average increases by one. What is the teacher's age in years?

  1. 31

  2. 36

  3. 51

  4. Cannot be determined

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

The total age of 36 students is 36 * 14 = 504. When the teacher is added, there are 37 people and the average becomes 15, giving a total sum of 37 * 15 = 555. The teacher's age is the difference between these two totals, which is 555 - 504 = 51.

Multiple choice maths average arithmetic mean of ap introduction to averages means

The average weight of 45 students in a class is 25 kg. Five of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class?

  1. $52\frac{1}{3}$
  2. $52\frac{1}{2}$
  3. $52\frac{2}{3}$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice maths average arithmetic mean of ap introduction to averages means

Four numbers are in proportion. The sum of the square of the four numbers is $50$ and the sum of the means is $5$. The ratio of first two terms is $1 : 3$. What is the average of the four numbers ?

  1. $2$
  2. $3$
  3. $5$
  4. $6$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the four numbers in proportion be a, b, c, d, meaning ad = bc. The sum of the means (b + c) is 5, and the sum of their squares is a^2 + b^2 + c^2 + d^2 = 50. Using the ratio of the first two terms a : b = 1 : 3, we can find the values of the terms, leading to numbers whose sum is 12 and average is 12 / 4 = 3.

Multiple choice maths average arithmetic mean of ap introduction to averages means

If the total incomes of $M,N,O,P$ are in the rate a $2:3:4:5$ and the total income of $M$ is $Rs\ 8000$ , then find approximate average salary of all four?

  1. $Rs\ 14000$
  2. $Rs\ 7000$
  3. $Rs\ 9950$
  4. $Rs\ 4875$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ratios 2:3:4:5. M = 2x = 8000, so x = 4000. Total = (2+3+4+5)x = 14x = 14 * 4000 = 56000. Average = 56000 / 4 = 14000.

Multiple choice

In a school, there are two sections, A and B, for Grade 7. In section A, the average percentage score for a test is 92, while in Section B, the average percentage score for the same test is 84. If the average score of all 40 students in the two sections is 89 percent, then how many students are there in section B?

  1. 10

  2. 12

  3. 15

  4. 20

  5. 25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let n be the number of students in section B. Then 40-n is the number in section A. Weighted average: (92(40-n) + 84n) / 40 = 89. 3680 - 92n + 84n = 3560. 120 = 8n. n = 15.

Multiple choice

A survey conducted on the income pattern of two kinds of customers; royal and premium of company X reveals that the average income of a customer is \$2,000 per month. If there are a total of 20 royal customers and their average income is \$1800, and if the ratio of royal and premium customers surveyed is 2 : 3, what is the average income of the premium customers per year?
  1. $23,000
  2. $24,500
  3. $25,600
  4. $27,600
  5. $30,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total customers = 20 (royal) + 30 (premium) = 50. Total income = 50 * 2000 = 100,000. Royal income = 20 * 1800 = 36,000. Premium income = 100,000 - 36,000 = 64,000. Average premium income per month = 64,000 / 30 = 2133.33. Yearly = 2133.33 * 12 = 25,600.

Multiple choice

A student was given the task to calculate the average marks of ten students of the class. It was known that none of the students scored less than 10 or greater than 100. By mistake, the student interchanged the 2 digits of the marks (mn) of one student. As a result, the average of marks calculated for the ten students was 2.7 more than what it would have been. What could be the value of n – m?

  1. 1

  2. 2

  3. 3

  4. 4

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

Let the marks be 10m + n. Interchanged, they become 10n + m. Difference = (10n + m) - (10m + n) = 9(n - m). The average change is 2.7, so the total sum change is 2.7 * 10 = 27. 9(n - m) = 27 => n - m = 3.

Multiple choice

Directions: A competitive firm sells his product at market price of Rs. 51 per unit. The fixed cost is Rs. 300 and variable cost for different levels of production are shown in the following table. Use table to answer the question. | Quantity | Variable cost (in Rs.) | Fixed cost | Total Cost | AVC | ATC | MC | | --- | --- | --- | --- | --- | --- | --- | | 0 10 20 30 40 50 | 0 470 980 1850 3400 5950 | | | | | | When production is 30 units, the average variable cost (in Rs.) is

  1. 70.6

  2. 60.6

  3. 61.6

  4. 71.6
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

The average mark scored by 50 students in a class was calculated to be 38. Later it was found that marks of two students were wrongly copied as 34 and 23 instead of 43 and 32. Find the correct average mark.

  1. 37.36

  2. 39.00

  3. 38.36

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial sum = 50 * 38 = 1900. Error: 34 and 23 were added instead of 43 and 32. Difference = (43 + 32) - (34 + 23) = 75 - 57 = 18. Correct sum = 1900 + 18 = 1918. Correct average = 1918 / 50 = 38.36.