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

P, Q and R have 50, a and b coins with them, respectively. If Q gives 15 coins to R, he is left with 1 3 the number of coins R has now. If together they had 50 more coins, the average number of all coins would have been 100. What is the value of a : b?

  1. 2 : 5

  2. 13 : 27

  3. 1 : 2

  4. 1 : 3

  5. 49 : 110
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

P=50, Q=a, R=b. Q gives 15 to R: R becomes b+15, Q becomes a-15. (a-15) = 1/3 * (b+15) => 3a - 45 = b + 15 => 3a - b = 60. Together they had 50 more coins: (50+a+b+50)/3 = 100 => 100+a+b = 300 => a+b = 200. Solving: 4a = 260 => a = 65. b = 135. a:b = 65:135 = 13:27.

Multiple choice

Directions: Each of the following questions consists of a question followed by three statements I, II and Ill. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. What is the age of a class teacher? I. There are 11 students in the class. II. The average age of the students and the teacher is 14 years. III. The average age of the teacher and the students is 3 years more than that of the students.

  1. Both I and III

  2. Both l and ll

  3. II and either I or III

  4. All I, II and III

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

Let T be the teacher's age and S be the sum of students' ages. Statement I gives the number of students (11). Statement II provides (S+T)/12 = 14, which is S+T = 168. Statement III provides (S+T)/12 = (S/11) + 3. With all three, we have a system of equations that allows solving for T.

Multiple choice

There are 60 students in a class. The average weight of the class increased by 200 g when a student weighing 45 kg left the class. What is the average weight of the remaining students?

  1. 57 kg

  2. 56.8 kg

  3. 58.2 kg

  4. 54 kg

  5. 52.3 kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the initial average be A. The total weight is 60A. After a 45 kg student leaves, the total weight is 60A - 45, and the new average is (60A - 45)/59. We are given (60A - 45)/59 = A + 0.2. Solving for A: 60A - 45 = 59A + 11.8, so A = 56.8 kg. The new average is 56.8 + 0.2 = 57 kg.

Multiple choice

Directions: You are given two quantities, Quantity I and Quantity II. Compare the two quantities and choose the correct option accordingly. Average age of the students of class A is 8 years and those of class B is 13 years. The average age of all the students together is 11 years. Quantity I: Number of students of Class A Quantity II: Number of students of Class B

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I = Quantity II

  4. No relation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

By alligation: (13-11) / (11-8) = 2/3. Ratio of Class A to Class B is 2:3. Since 2 < 3, Quantity I < Quantity II.

Multiple choice

In a group of junior basketball players, the average weight of boys is 65.9 kg and the average weight of girls is 57 kg. When the average weight of both boys and girls is 60.3 kg and the total number of boys in the group is 66, then what is the total number of girls in the group?

  1. 112

  2. 154

  3. 162

  4. 168

  5. 180
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using alligation: Boys (65.9), Girls (57), Mean (60.3). Boys ratio = 60.3 - 57 = 3.3. Girls ratio = 65.9 - 60.3 = 5.6. Ratio Boys:Girls = 3.3:5.6 = 33:56. If 33 units = 66 boys, then 1 unit = 2 boys. Girls = 56 * 2 = 112.

Multiple choice

Directions: In this question, two Quantities I and II are given. You have to solve both the Quantities to establish the correct relation between Quantity I and Quantity II and choose the correct option. Pal travels by bus to school at an average speed of 40 kilometres per hour. He is driven home by the same route in his mother's car at an average speed of 50 kilometres per hour. Quantity I: Average speed for both parts of the journey Quantity II: 45 km/hr

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity II ≥ Quantity I

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

Average speed = 2xy / (x+y) = 2 * 40 * 50 / (40+50) = 4000 / 90 = 44.44 km/hr. Quantity I (44.44) < Quantity II (45).

Multiple choice

In the 2010 - 2012 batch of Sloan School of Management, the average marks of a student for the third semester were 70. If he had obtained 20 marks more in Financial Management paper, 2 marks more in his TQM paper and 6 marks more in Business Management paper, his average/paper would have been 72. How many papers did he take in the third semester?

  1. 8

  2. 9

  3. 10

  4. 14
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let n be the number of papers. Total marks = 70n. New total = 70n + 20 + 2 + 6 = 70n + 28. New average = 72, so (70n + 28)/n = 72. 70n + 28 = 72n. 2n = 28, n = 14.