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

Passage

Directions: Read the given graphs carefully and answer the question. The given pie chart shows the percentage break up of smart watches sold by XYZ company to 5 showrooms in a particular city. The total revenue generated by the XYZ company is Rs. 20,00,000. It is given that XYZ company manufactures 5 models of smart watches and each model is sent to different showrooms. The table shows the number of defective smart watches. Showroom Number of Defective Smart Watches Showroom -1 18 Showroom -2 13 Showroom -3 26 Showroom -4 10 Showroom -5 29 According to the company policy, no smart watch will be replaced or changed irrespective of its working condition.

What was the average number of smart watches sold per showroom, if the smart watches were sold at Rs. 4,000 each?

  1. 100

  2. 120

  3. 90

  4. 80

  5. 150
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total revenue = 20,00,000. Price per watch = 4,000. Total watches sold = 20,00,000 / 4,000 = 500. There are 5 showrooms. Average = 500 / 5 = 100.

Multiple choice

Passage

A, B, C, D, E, F and G are cousins. D is thrice as old as A. Further, C is as many years younger to B, as G to E and E to D. The average age of D and G is 16 years; the average age of A and E is 11 years; the average age of B and C is also 11 years. B and C have equal weight. A's weight is 10 kg less than that of B; D is 4 kg heavier than E; E is 4 kg heavier than F; F is 4 kg heavier than G. Further, D has age-weight ratio of 9 : 20, where age is in years and weight in kg; A has age-weight ratio of 2 : 5. Moreover, none of them is more than 40 kg.

What is the average age (in years) of B, C, D, E and G?

  1. 12

  2. 13

  3. 14

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

Solving the system of equations based on the passage: D=3A, C=B-(G-E), G-E=E-D, (D+G)/2=16, (A+E)/2=11, (B+C)/2=11. From these, D+G=32, A+E=22, B+C=22. The average of B, C, D, E, G is (B+C+D+E+G)/5. Since B+C=22 and D+G=32, we need E. Using D=3A and D+G=32, and E-D=G-E => 2E=D+G=32, so E=16. Then A = (22-16)=6. D = 3*6=18. G = 32-18=14. Sum = 22 + 32 + 16 = 70. Average = 70/5 = 14.

Multiple choice

Passage

A, B, C, D, E, F and G are cousins. D is thrice as old as A. Further, C is as many years younger to B, as G to E and E to D. The average age of D and G is 16 years; the average age of A and E is 11 years; the average age of B and C is also 11 years. B and C have equal weight. A's weight is 10 kg less than that of B; D is 4 kg heavier than E; E is 4 kg heavier than F; F is 4 kg heavier than G. Further, D has age-weight ratio of 9 : 20, where age is in years and weight in kg; A has age-weight ratio of 2 : 5. Moreover, none of them is more than 40 kg.

Consider the following statements: 1. The age of F cannot be determined due to insufficient data. 2. The average weight of D and F is equal to weight of E. 3. The weight difference is maximum for D and A. Which of the statements given above are correct?

  1. 1 and 2 only

  2. 2 and 3 only

  3. 1 and 3 only

  4. 1, 2 and 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

By solving the age equations, we find A = 6, D = 18, E = 16, G = 14, B = 12, and C = 10, but there is no information to determine F's age, making Statement 1 correct. For weights, using the ratios and differences, we find W_D = 40, W_E = 36, W_F = 32, W_G = 28, W_A = 15, and W_B = W_C = 25. Thus, the average of W_D and W_F is 36 (equal to W_E), and the maximum weight difference is indeed between D (40) and A (15), making Statements 2 and 3 correct as well.

Multiple choice

Passage

Directions: Each question below is followed by two statements, I and II. You are to determine whether the data in the statements is sufficient to answer the question.

Question: What is the average height of a group of 10 students? Statements: I. The sum of the heights of all 10 students is 1650 cm. II. The shortest student in the group is 150 cm tall, and the tallest student is 180 cm tall.

  1. Statement I alone is sufficient to answer the question.

  2. Statement II alone is sufficient to answer the question.

  3. Both statements I and II together are sufficient to answer the question, but neither statement alone is sufficient.

  4. Each statement alone is sufficient to answer the question.

  5. Statements I and II together are not sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The average is defined as the sum of values divided by the count. Statement I provides the sum (1650) and the count (10), which is sufficient to calculate the average (165). Statement II provides the range, which does not allow for the calculation of the average.

Multiple choice

Passage

Directions: The table below gives the percentage of marks obtained by 6 students in 6 subjects in an examination. Answer the following question based on the data given in the table. The numbers in brackets are the maximum marks in each subject. Student Subjects (Max. Marks) Physics (120) Biology (120) Maths (120) Geology (120) Economics (120) English (120) A 70 75 70 65 60 70 B 80 70 75 60 50 75 C 75 72 71 70 60 65 D 60 70 65 55 60 70 E 70 75 65 50 55 60 F 65 70 60 65 50 60

Find the average marks obtained by a student in Economics and Physics, respectively.

  1. 84, 67

  2. 65, 83

  3. 66, 85

  4. 67, 84
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Passage

Students' Scores in Mathematics, Science and English in a Class Student Mathematics Science English A 85 80 82 B 90 85 88 C 78 75 76 D 88 90 85 E 92 94 90

What is the overall average English score of the five students?

  1. 82.5

  2. 84.2

  3. 84.5

  4. 85.2

  5. 86
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

English scores are 82, 88, 76, 85, 90. Sum = 82 + 88 + 76 + 85 + 90 = 421. Average = 421 / 5 = 84.2.

Multiple choice

Passage

Number of units (in hundreds) of five different types of sports equipment sold by a store from 2018 to 2022 Year Football Basketball Tennis Rackets Cricket Bats Badminton 2018 25 18 12 20 15 2019 30 22 14 23 17 2020 35 26 18 25 20 2021 38 28 20 27 23 2022 40 30 22 29 25

What is the average number of units sold per year (in hundreds) for Football and Badminton combined over the five-year period?

  1. 2,540

  2. 5,240

  3. 5,360

  4. 6,430

  5. 8,280
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Passage

Directions: Refer to the data below and answer the question that follows. Jason organised the first 16 natural numbers into a 4 × 4 grid, placing one number in each cell of the grid. The rows of the grid were labelled A, B, C, and D (from top to bottom), while the columns were labelled P, Q, R, and S (from left to right). For instance, the number 9 was organised in cell AR. The total of the four numbers in rows B, C, and D was 29, 36, and 22, respectively. Similarly, the sum of the four numbers in columns P, Q, and R was 31, 23, and 44, respectively. The partially filled table is given below: P Q R S A 11 9 B 5 4 C 16 D 3 12

What is the average of the numbers in row A?

  1. 7.75

  2. 9.25

  3. 11.75

  4. 12.25

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

The sum of all numbers 1-16 is 136. Rows B+C+D sum to 29+36+22 = 87. Row A sum = 136 - 87 = 49. Average = 49/4 = 12.25.

Multiple choice

Passage

Directions: Study the following information carefully and answer the question. There are 7 persons, namely, A, B, C, D, E, F and G. They all are made to stand according to their weights in descending order from left to right. B is the second lightest person. A weighs between G and B. F is the heaviest. D has an equal number of persons on either side who are heavier and lighter than him. D has a weight of 85 kg. E is immediate heavier than B. A is heavier than C. The lightest person has a weight of 65 kg.

What is the average weight of D and C?

  1. 80 kg

  2. 75 kg

  3. 65 kg

  4. 50 kg

  5. 85 kg
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Ordering by weight (descending): F > D > A > G > E > B > C. D is 85kg. Lightest (C) is 65kg. Average of D and C = (85 + 65) / 2 = 75kg.

Multiple choice

Passage

Directions : Study the following information and answer the question that follows. Five persons − Harry, Rose, Emily, Sean and William − are playing a game in which they have to enter some number (input), and the output generated is distinct each time. The output would be bigger than the number entered. Every person gets one chance and they enter a distinct number. Also, the difference between the input number and the output number is also different for every person. The input numbers, the output numbers and the difference between the input and output numbers are all positive integral multiples of 5. The following information is known about the input, the output and the difference between the input and output numbers for each person: (1) Rose's input number is 20 and the difference between the input and output numbers of Rose is 5 more than the difference between the input and output numbers of Emily. (2) Harry's output number is 50 and his input number is 5 more than the input number of Sean. (3) The output number of William is at least 45, while the input number for him is at least 25. (4) The input number of any of the five persons is not greater than 40, while the output number of any of the five persons is not greater than 55. (5) The difference between the input and output numbers of Rose is 10 more than the difference between the input and output numbers of Sean. (6) Emily's output number is 35 and the difference between the input and output numbers of Emily is 20 less than the difference between the input and output numbers of Harry.

The average input number is how much percent less than average output numbers for all the friends combined?

  1. 26.29%

  2. 36.43%

  3. 41.36%

  4. 63.41%
Reveal answer Fill a bubble to check yourself
D Correct answer
Multiple choice

Passage

Directions: Read the following and answer the question. Each of six persons - Madison, Lucas, Andrew, Faith, Marie and Amber - travels between exactly two localities, i.e. one locality is where the person lives and the other locality where he works from among six different localities - L1, L2, L3, L4, L5 and L6 - such that no two persons live in the same locality and no two persons work in the same locality. Further, no two persons travel between the same pair of localities. It is also known that the travel time, i.e. the time taken by a person to travel from home to workplace (calculated in minutes), is a distinct positive integer less than 8. The following information is known about home, workplace and travel time of six persons. (1) The workplace of Madison is the same as the home of Faith, but neither of these persons travels either from L2 or to L2. (2) The travel time of Marie is 2 minutes more than that of Andrew. (3) One of the persons lives in L1 and works in L6, with a travel time of three minutes. (4) The travel time of Amber, who works in L3, is less than 7 minutes, while the travel time of the person who lives in L3 is 2 minutes. (5) The travel time of Lucas, who lives in L5, is the average of the travel times of the persons who live in L4 and L6. (6) The person who works in L2 lives in L3, while Faith does not live in L6.

Find the average travel time taken by all the six persons.

  1. 3.7 minutes

  2. 4.5 minutes

  3. 5.4 minutes

  4. None of these

  5. a
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

Passage

Directions: The following table gives the marks obtained by six students in six different subjects in an examination. The maximum marks for each subject are given in the brackets. Students Subjects (Max. Marks) Hindi (120) English (130) Math (150) Economics (140) Accountancy (160) Geography (100) Aman 95 65 115 100 125 90 Kartik 60 95 130 95 100 80 Mukesh 105 90 95 110 140 85 Lokesh 55 115 60 65 75 70 Summit 75 85 75 80 95 75 Sandhya 85 110 120 130 130 95

What is the average of total marks obtained by Aman, Kartik, Mukesh and Lokesh in all subjects?

  1. 523.25

  2. 493.75

  3. 463.25

  4. 553.75
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum for Aman: 95+65+115+100+125+90 = 590. Kartik: 60+95+130+95+100+80 = 560. Mukesh: 105+90+95+110+140+85 = 625. Lokesh: 55+115+60+65+75+70 = 440. Total sum = 590+560+625+440 = 2215. Average = 2215 / 4 = 553.75.