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 number of children in a camp is x and their average weight is 20 kg. If 5 children, each weighing 12 kg, join the camp or if 10 children, each weighing 21 kg, leave the camp, then the average weight in both the cases remains the same. The value of x is

  1. 18

  2. 16

  3. 15

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

Let x be the number of children. The total weight is 20x. Setting up the equations for the two scenarios: (20x + 5*12)/(x+5) = 20 and (20x - 10*21)/(x-10) = 20. Solving either yields x = 15.

Multiple choice

Directions: A frequency distribution data is given below. Look at it carefully and answer the given question. | Age (in years) | : | 8 | 20 | 26 | 29 | | --- | --- | --- | --- | --- | --- | | Number of persons | : | 3 | 2 | m | 1 | If the average age is 17 years, then what is the value of m?

  1. 1

  2. 2

  3. 3

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

The average age is the total sum of ages divided by the total number of people. Setting up the equation (8 * 3 + 20 * 2 + 26 * m + 29 * 1) / (3 + 2 + m + 1) = 17 simplifies to (93 + 26m) / (6 + m) = 17, which gives 9m = 9, so m = 1.

Multiple choice

The average of 18 numbers is 52. The average of the first 8 numbers is 62 and the average of the next 7 numbers is 45. If the 16th number is 6 less than the 17th number and the 17th number is one more than the 18th number, then what is the average of the 16th and 18th numbers?

  1. 39

  2. 39.5

  3. 40.5

  4. 40
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sum of 18 = 18 * 52 = 936. Sum of first 8 = 8 * 62 = 496. Sum of next 7 = 7 * 45 = 315. Sum of 16th, 17th, 18th = 936 - 496 - 315 = 125. Let 18th = x, 17th = x+1, 16th = x+1-6 = x-5. 3x - 4 = 125, 3x = 129, x = 43. 16th = 38, 18th = 43. Average = (38 + 43) / 2 = 40.5.

Multiple choice

The average weight of a sample of 10 apples is 52 g. Later, it is found that the weighing machine has shown the weight of each apple 10 g less. The correct average weight of an apple is

  1. 62 g

  2. 42 g

  3. 50 g

  4. 52 g
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

If the machine showed 10g less for each of the 10 apples, the total weight was underestimated by 10 * 10 = 100g. The correct total weight is (10 * 52) + 100 = 620g. The correct average is 620 / 10 = 62g.

Multiple choice

The average age of 65 boys of a class is 14 years. In which, average age of 20 boys is 14 years and average age of 15 other boys is 12 years. Find the average age of remaining boys.

  1. 16 years

  2. 13 years

  3. 17 years

  4. 15 years

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

Total age of 65 boys = 65 × 14 = 910 years. Age of 20 boys = 20 × 14 = 280 years. Age of 15 boys = 15 × 12 = 180 years. Age of remaining 30 boys = 910 - 280 - 180 = 450 years. Average age of remaining boys = 450/30 = 15 years.

Multiple choice

\text{The average of five numbers is 51.4. The average of first and second number is 30.5. The average of fourth and fifth number is 62. What is the third number?}

  1. 72

  2. 75

  3. 77

  4. 78

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

Sum of five numbers = 5 × 51.4 = 257. Sum of first and second = 2 × 30.5 = 61. Sum of fourth and fifth = 2 × 62 = 124. Third number = Total - (Sum of 1st & 2nd) - (Sum of 4th & 5th) = 257 - 61 - 124 = 72. Option A is correct.

Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question ? What is the age of C in a group of A, B, C, D and E whose average age is 45 years? (I) Average of the ages of A and B is 53 years. (II) Average of the ages of D and E is 47 years.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statement together are sufficient, but neither statement alone is sufficient.
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

We know A+B+C+D+E = 45 × 5 = 225 years. Statement I gives A+B = 53 × 2 = 106 years. Statement II gives D+E = 47 × 2 = 94 years. Using both: C = 225 - (A+B) - (D+E) = 225 - 106 - 94 = 25 years. Neither statement alone is sufficient, but together they give the answer.