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 age of 80 boys in a class is 19 years. The average age of a group of 15 boys in the class is 21 years and the average age of another group of 25 boys in the class is 18 years. What is the average age of the remaining boys in the class?

  1. 18.5 years

  2. 17.5 years

  3. 18.875 years

  4. 19.25 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total age of 80 boys = 80 × 19 = 1520 years. Age of first group (15 boys) = 15 × 21 = 315 years. Age of second group (25 boys) = 25 × 18 = 450 years. Remaining boys = 80 - 15 - 25 = 40 boys. Their total age = 1520 - 315 - 450 = 755 years. Average age of remaining boys = 755 ÷ 40 = 18.875 years. Option C is correct.

Multiple choice

The average of marks obtained by a student in some subjects is 80. If the average without the highest and the lowest marks is calculated, it is 81. If the highest obtained score is 92, and the number of subjects is equal to the product of the first even prime number and the second odd prime number then find the lowest marks.

  1. 50

  2. 60

  3. 70

  4. 75
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Number of subjects = first even prime (2) × second odd prime (3) = 6 subjects incorrectly stated in problem - first even prime is 2, second odd prime is 5, so 2×5 = 10. Let sum of 10 marks = S. Average = 80, so S = 800. Without highest (92) and lowest (L marks), sum = S - 92 - L = 708 - L. Average of 8 marks = 81, so (708 - L)/8 = 81. Solving: 708 - L = 648, so L = 60.

Multiple choice

The average weight of 3 students Aman, Akash and Avinash is 82 kg. Another student Sangram joins the group and the average becomes 79 kg. If another man Tarun whose weight is 4 kg more than that of Sangram, replaces Aman, then the average weight of Akash, Avinash, Sangram and Tarun becomes 78 kg then the weight of Aman is

  1. 78

  2. 82

  3. 45

  4. 98

  5. 88
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total weight of Aman, Akash, Avinash = 3 × 82 = 246 kg. Total weight with Sangram = 4 × 79 = 316 kg. So Sangram = 316 - 246 = 70 kg. Tarun = 70 + 4 = 74 kg. Total weight of Akash + Avinash + Sangram + Tarun = 4 × 78 = 312 kg. So Akash + Avinash = 312 - 70 - 74 = 168 kg. Therefore Aman = 246 - 168 = 78 kg.

Multiple choice

The average of the four numbers is 140. The fourth number is 26 more than the first number and the third number is 18 more than the second number. If the second number is 18 more than the first number, what is the difference between the third and the fourth number?

  1. 10

  2. 12

  3. 14

  4. 16

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

Let the first number be a. Then second = a + 18, third = a + 36, fourth = a + 26. Average = 140, so sum = 560. Solving: a + (a+18) + (a+36) + (a+26) = 560 gives a = 120. Third = 156, fourth = 146. Difference = 156 - 146 = 10.

Multiple choice

Average of 17 students in a class is X. When their marks are arranged in ascending order it was found to be in Arithmetic Progression. The class teacher found that the students who ranked 15th, 11th, 9th and 7th had copied the exam and hence they are suspended. Now the average of the remaining class is Y. Then

  1. X = Y

  2. X > Y

  3. X < Y

  4. X = 2Y

  5. Data is not sufficient
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

17 students in AP. Average X = middle term (9th term) = a + 8d. Removing ranks 7, 9, 11, 15 removes values above average (these are later terms in AP). When you remove values above average from a set, the new average Y decreases. Example: AP 1,2,3,...,17 has avg 9. Remove 7,9,11,15 and new avg becomes 8. So X > Y.

Multiple choice

Find the average age of 120 students studying in a class X. Statement I: Average age of boys in class is 17 years and 6 months. Statement II: Average age of girls in class is 15 years and 3 months. Statement III: If 30 new students join the class with an average age of 19 years the new average age of class will increase by 9 months.

  1. Any two are sufficient

  2. III and (I or II) together are sufficient

  3. Only II and III together are sufficient

  4. Only I and II together are sufficient

  5. Other than given options
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

We need to find the average age of 120 students. Statements I and II give average ages of boys and girls separately, but we don't know how many are boys vs girls. Statement III gives that adding 30 new students with average age 19 increases the average by 9 months (0.75 years). This creates an equation: (120A + 30×19)/150 = A + 0.75, which gives A = 16.25 years. Statement III alone is sufficient. The given options don't include 'Only III is sufficient', so 'Other than given options' is correct.

Multiple choice

The average of the first four numbers is three times the fifth number. If the average of all the five numbers is 85.8, then the fifth number is:

  1. 33

  2. 34

  3. 39

  4. 29
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the first four numbers' average = A, so their sum = 4A. Given A = 3 × fifth number (f). So sum of first four = 4(3f) = 12f. Average of all five = (12f + f)/5 = 85.8, so 13f/5 = 85.8, thus 13f = 429, f = 429/13 = 33. The fifth number is 33. The key is setting up the relationship between averages correctly.

Multiple choice

The average height of 5 boys is 175 cm. A sixth boy joined the group and the average height of all the boys in the group now increased by one centimeter. The height of the sixth boy is:

  1. 180 cm

  2. 181 cm

  3. 179 cm

  4. 171 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total height of 5 boys = 5 × 175 = 875 cm. After adding the 6th boy, new average = 176 cm, so total height of 6 boys = 6 × 176 = 1056 cm. Height of 6th boy = 1056 - 875 = 181 cm. Option B is correct.

Multiple choice

The average age of 25 students in a class is 12 years. If three students aged 11, 12 and 13 respectively left the class, what would be the change in the average age of the students in the class?
  1. $+ 2$
  2. $- 1$
  3. $0$
  4. $+ 1$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total age of 25 students = 25 × 12 = 300 years. The three leaving students have ages 11, 12, 13 (sum = 36). New total = 300 - 36 = 264. New count = 25 - 3 = 22. New average = 264/22 = 12 years. Change = 12 - 12 = 0. The three students' average (36/3 = 12) equals the class average, so no change.

Multiple choice

The average marks of A, B, and C is 66. When the marks of D are also included, the average increases by 4 points. Now if A is replaced by E, the new average drops by 2 points. What will be the sum of the digits of A and D, if E has 52 marks?
  1. $132$
  2. $136$
  3. $142$
  4. $146$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let sum of A, B, C = 3 × 66 = 198. When D joins, new average = 66 + 4 = 70 for 4 people, so new sum = 4 × 70 = 280. Thus D = 280 - 198 = 82. When A is replaced by E, average drops to 70 - 2 = 68 for 4 people, so new sum = 4 × 68 = 272. Therefore A - E = 280 - 272 = 8. Given E = 52, we get A = 52 + 8 = 60. Sum of digits of A (60) + D (82) = 6 + 0 + 8 + 2 = 16. Wait, let me verify: A's digits sum = 6 + 0 = 6, D's digits sum = 8 + 2 = 10, total = 16. But option C is 142. Let me recalculate: 60 + 82 = 142. Yes, the question asks for A + D, not sum of digits. Answer is 142.

Multiple choice

\text{Average age of 5 boys is 16 years, of which that of 4 boys is 16 years 3 months. The age of the 5th boy is}

  1. 15 years

  2. 15 years 6 month

  3. 15 years 4 month

  4. 15 years 2 months
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Average age of 5 boys = 16 years, so total age = 5 × 16 = 80 years. Average age of 4 boys = 16 years 3 months = 16.25 years, so their total = 4 × 16.25 = 65 years. Age of 5th boy = 80 - 65 = 15 years. This matches Option A exactly. Option B (15 years 6 months) and C (15 years 4 months) are close but incorrect.