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 of 5 numbers is 65. The average of the first two numbers is 81 and the average of the last two numbers is 38. What is the third number?

  1. 63

  2. 87

  3. 99

  4. 54
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The average of 5 numbers is 65, so their sum is 5 × 65 = 325. The first two numbers average to 81, so their sum is 2 × 81 = 162. The last two numbers average to 38, so their sum is 2 × 38 = 76. Therefore, the third number = Total sum - (Sum of first two + Sum of last two) = 325 - (162 + 76) = 325 - 238 = 87.

Multiple choice

In a group of 12 students, the average age is increased by 2 years when three of them are replaced by 5 students, and the total age increased by 50 years. Then what is the sum of their ages?

  1. 132

  2. 154

  3. 172

  4. 182
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Original: 12 students, total age = 12A. New: 14 students (3 replaced by 5), total age = 12A + 50, average = A + 2. So (12A + 50)/14 = A + 2, giving 12A + 50 = 14A + 28, so 2A = 22 and A = 11. New total sum = 12(11) + 50 = 182. Option D is correct.

Multiple choice

The average age of 75 boys in a hall is 25 years and the average age of 20 boys of that hall is 12 years whereas the average age of 10 boys of that hall is 15 years. Thus, find the average age of remaining boys of the hall?

  1. 30years

  2. 28 years

  3. 33 years

  4. 35 years

  5. 37 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let total boys = 75, average age = 25 years. Total age = 75 × 25 = 1875 years. Given: 20 boys average = 12 years, total age = 20 × 12 = 240 years. 10 boys average = 15 years, total age = 10 × 15 = 150 years. Remaining boys = 75 - 20 - 10 = 45 boys. Total age of remaining = 1875 - 240 - 150 = 1485 years. Average of remaining = 1485 ÷ 45 = 33 years.

Multiple choice

The average of the squares of five consecutive positive integers is 66. Find the average of these five integers.

  1. 6

  2. 10

  3. 8

  4. 12
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the middle integer be n. Then the integers are n-2, n-1, n, n+1, n+2. Their squares are (n²-4n+4), (n²-2n+1), n², (n²+2n+1), (n²+4n+4). Sum = 5n² + 10. Average = (5n² + 10)/5 = n² + 2 = 66, so n² = 64, n = 8. The average of the five integers is n = 8. Option C is correct.

Multiple choice

In a cricket team of 11 boys, one player weighing 42 kg is injured and his place is taken by another player. If the average weight of the team, as a result of this, is increased by 100 grams, then the new player weighs.
  1. $44.0 kg.$
  2. $42.1 kg.$
  3. $43.1 kg.$
  4. $44.4 kg.$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original average = x kg. Original total = 11x. New total = 11(x + 0.1) = 11x + 1.1. New player = (11x - 42) + 1.1 = 11x - 40.9. But wait, the increase is 100 grams = 0.1 kg per person, so total increase = 11 × 0.1 = 1.1 kg. New player weight = 42 + 1.1 = 43.1 kg. The average increased, so new player must be heavier.

Multiple choice

If the average height of men in a hall is (180) cm and that of women is (150) cm if the average height of the gathering is (165) cm, then find the number of women present in the hall if the number of men present in the hall are (78)?

  1. 68

  2. 78

  3. 58

  4. 88

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

Let w = number of women. Using weighted average formula: (180×78 + 150×w)/(78+w) = 165. Multiply both sides: 14040 + 150w = 165(78+w) = 12870 + 165w. Rearranging: 14040 - 12870 = 165w - 150w, so 1170 = 15w, giving w = 78.

Multiple choice

The average weight of 15 students in a class increases by 1.5 kg when one of the students weighing 40 kg is replaced by a new student. What is the weight (in kg.) of the new student?
  1. $64.5$
  2. $56$
  3. $60.5$
  4. $62.5$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When the average of 15 students increases by 1.5 kg, the total weight increases by 15 × 1.5 = 22.5 kg. The new student must weigh 22.5 kg more than the student they replaced (40 kg). Therefore, new student's weight = 40 + 22.5 = 62.5 kg. This is a standard average replacement problem where the change in total equals the number of items multiplied by the change in average.

Multiple choice

In an examination, the average marks of girls is 73 and the average marks of boys is 71. The average marks of girls and boys together is 71.8. What is the percentage of boys ?

  1. 58

  2. 60

  3. 55

  4. 40

  5. 45
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Using the alligation method: Let the ratio of girls:boys be x:y. Then 73x + 71y = 71.8(x+y). Solving gives 73x + 71y = 71.8x + 71.8y, which simplifies to 1.2x = 0.8y, so x/y = 2/3. This means girls:boys = 2:3, so boys = 3/(2+3) = 3/5 = 60%.

Multiple choice

The average weight of all the students in a certain class is 60 kg. The average weight of the boys from the class is 70 kg. While that of the girls is 55 kg. What is the ratio of number of boys to that of girls ?

  1. 2 : 1

  2. 1 : 2

  3. 1 : 4

  4. 4 : 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let B and G be the number of boys and girls, and W = B + G be total students. 60W = 70B + 55G. Substituting W = B + G: 60(B + G) = 70B + 55G, so 60B + 60G = 70B + 55G, giving 5G = 10B, or G = 2B. Therefore, B : G = 1 : 2.

Multiple choice

The average of first four of five numbers is 26 and that of the last four is 25. The difference between the last number and the first number is

  1. 1

  2. 4

  3. 5

  4. 16
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the five numbers be a, b, c, d, e. Average of first four: (a+b+c+d)/4 = 26, so a+b+c+d = 104. Average of last four: (b+c+d+e)/4 = 25, so b+c+d+e = 100. Subtracting: (a+b+c+d) - (b+c+d+e) = 104 - 100, giving a - e = 4. Therefore e - a = -4, meaning the last number is 4 less than the first number.

Multiple choice

There were 35 students in a hostel. Due to the admission of 7 new students the expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. What was the original expenditure of the mess ?

  1. 420

  2. 320

  3. 450

  4. 500
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let original expenditure be E for 35 students. New expenditure = E + 42 for 42 students. New average = (E+42)/42. Original average = E/35. Given: (E+42)/42 = E/35 - 1. Solving: E+42 = 42(E/35 - 1) = 6E/5 - 42. So E + 84 = 6E/5, giving 5E + 420 = 6E, thus E = 420.

Multiple choice

Six articles have an average weight of 167 grams. An article with weight 162 grams is excluded from the group. Find the new average weight

  1. 168 grams

  2. 166 grams

  3. 167 grams

  4. 165 grams
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total weight of 6 articles = 6 × 167 = 1002 grams. After removing 162 gram article, new total = 1002 - 162 = 840 grams. New average = 840/5 = 168 grams. The average increases because the removed article weighs less than the original average.