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 a warehouse, there are eight crates of fruits. The weight of the first crate is 200 kg, and the weight of the second crate is 30% more than the weight of the third crate, which is 15% less than the weight of the first crate. The fourth crate weighs the average of the first and third. The fifth crate weighs the average of the second and fourth. The sixth crate weighs 10% more than the third. The weight of the seventh crate is equal to the average weight of the second and fifth crates, and the weight of the eighth crate is equal to the average weight of all the other crates excluding the second and seventh crate. Find the average of the average weight of the five lighter crates and the average weight of the five heavier crates.

  1. 189.35 kg

  2. 186 kg

  3. 195.60 kg

  4. 276 kg

  5. 391.20 kg
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Crate 1 = 200. Crate 3 = 200 * 0.85 = 170. Crate 2 = 170 * 1.3 = 221. Crate 4 = (200 + 170) / 2 = 185. Crate 5 = (221 + 185) / 2 = 203. Crate 6 = 170 * 1.1 = 187. Crate 7 = (221 + 203) / 2 = 212. Crate 8 = (200 + 170 + 185 + 203 + 187) / 5 = 189. The weights are 200, 221, 170, 185, 203, 187, 212, 189. Sorted: 170, 185, 187, 189, 200, 203, 212, 221. The five lighter are 170, 185, 187, 189, 200 (avg 186.2). The five heavier are 189, 200, 203, 212, 221 (avg 205). The average of these two averages is (186.2 + 205) / 2 = 195.6.

Multiple choice

In a classroom, the average score of nine students in a test is 75 marks. Each student achieved a distinct positive integer score, with each score being at least 70 marks and not exceeding 100 marks, the maximum possible score. What is the second-highest possible score that a student could have achieved?

  1. 99

  2. 97

  3. 87

  4. 81

  5. 77
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The sum of 9 scores is 9 * 75 = 675. To maximize the second-highest score, we must minimize the other 8 scores. The smallest distinct scores starting from 70 are 70, 71, 72, 73, 74, 75, 76, 77. Their sum is 588. The remaining score is 675 - 588 = 87. If the highest score is 100, the next highest could be 87. If we adjust to keep scores distinct and under 100, 81 is a possible value for the second highest.

Multiple choice

In a class test, four students — P, Q, R, and S — each secured an integer score out of 10 (repetition of marks allowed). The sum of P's marks and the average of the marks obtained by Q, R, and S is 9. The sum of Q's marks and the average of the marks of P, R, and S is 15. The sum of R's marks and the average of the marks of P, Q, and S is 11. It is also known that the sum of P's marks and twice of R's marks is 9. What is the average score of all four students?

  1. 5.25

  2. 5.75

  3. 6.25

  4. 6.75
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

In a non-decreasing list of N real numbers, the average is 599. If the first element of the list is replaced with four times its original value, the new average increases to 800. How many different values can the first element in the list take?

  1. 3

  2. 5

  3. 7

  4. 11
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the sum of N numbers be S. S/N = 599, so S = 599N. Let the first element be x. The new sum is S - x + 4x = S + 3x. The new average is (S + 3x)/N = 800. Substituting S, 599N + 3x = 800N, so 3x = 201N, or x = 67N. Since the list is non-decreasing, x must be <= 599. Thus 67N <= 599, meaning N can be 1, 2, 3, 4, 5, 6, 7, 8. There are 8 possible values for N, but the problem implies specific constraints on N.

Multiple choice

The average of a group of 15 members initially increases from 60kg to 65 kg when A, B and C join the group. The weight of A, B and C are in the ratio 3 : 4 : 2. What is the difference between weight of A and C?

  1. 40 kg

  2. 45 kg

  3. 20 kg

  4. 30 kg
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial sum = 15 * 60 = 900. New sum = 18 * 65 = 1170. Sum of A, B, C = 1170 - 900 = 270. Ratio 3:4:2 means 9 parts = 270, so 1 part = 30. A = 3*30=90, C = 2*30=60. Difference = 30.

Multiple choice

The students of a class are divided into 3 groups depending on their performance in a test – the top, middle and bottom. The top group consists of 45% of the students, the middle group consists of 30% of the students and the rest are in the bottom group. The average marks of the bottom group are 20, those of the middle are 25 while the average marks for the entire class are 26. Find the average marks of the top group.

  1. 7

  2. 12

  3. 22

  4. 30
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let total students be 100. Top=45, Middle=30, Bottom=25. Total marks = 100 * 26 = 2600. Bottom marks = 25 * 20 = 500. Middle marks = 30 * 25 = 750. Top marks = 2600 - 500 - 750 = 1350. Average of top = 1350 / 45 = 30.

Multiple choice

On the occasion of teacher's day, some number of boys and girls contributed some money. The average contribution of boys was Rs. 250 and that of girls was Rs. 100. If the average contribution per student was Rs. 160 on the whole then what percent of students are boys?

  1. 60%

  2. 44%

  3. 40%

  4. 80%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let B be number of boys, G be number of girls. 250B + 100G = 160(B+G). 250B + 100G = 160B + 160G. 90B = 60G. B/G = 60/90 = 2/3. Boys as percentage of total = 2/(2+3) = 2/5 = 40%.

Multiple choice

A college has raised 50% of the amount it needs for a new building by recieving an average donation of 600 rs. from the people already solicited. The people was 40% of the total people. If the college has to raise exactly the amount needed for new building what should be the average donation from the remaining people?

  1. 300 rs

  2. 250 rs

  3. 400 rs

  4. 500 rs

  5. 450 rs.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If 40% of the people raised 50% of the required amount, their average donation of Rs. 600 implies a total target of Rs. 48,000 per 100 people. The remaining 60% must raise the other Rs. 24,000, requiring an average donation of Rs. 400.

Multiple choice

Twelve students lived in a hostel, and 9 years ago, the combined total of their ages was 190 years.5 years after that, one person aged 24 leaves the hostel and a new person of age 18 years joined the hostel. Then after another 2 years , another person of 24 years leaves the hostel , and again, a new person of 20 years joined the hostel. The current average age of 12 students in the hostel ?

  1. 24 years

  2. 20 years

  3. 16 years

  4. 12 years

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

Total age 9 years ago was 190. 9 years later (current), total age would be 190 + (12 * 9) = 298. Accounting for the replacements: -24+18 (net -6) and -24+20 (net -4), total is 298 - 10 = 288. Average = 288/12 = 24.