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

While finding the average of ten two-digit odd numbers, a student by mistake took the reverse of one of the numbers, as a result of which the average went up by 2.7. What is the absolute difference between the units and the tens digit of that number?

  1. 9

  2. 2

  3. 3

  4. 4

  5. 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the number be 10x + y. Reverse is 10y + x. Difference in sum = (10y + x) - (10x + y) = 9(y - x). Average increase = 2.7, so total sum increase = 2.7 * 10 = 27. 9(y - x) = 27, so y - x = 3.

Multiple choice

In a middle school there were initially 12 teachers. If three teachers with ages 32 years, 34 years and 40 years left the school, the average age of the rest of the teachers reduced by 3. What was the average age(in years) of 12 teachers?

  1. 79/3

  2. 133/3

  3. 127/3

  4. 145/3

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

Let the average age of 12 teachers be A. Total age = 12A. After 3 teachers (32, 34, 40) leave, total age = 12A - 106. New average = (12A - 106) / 9 = A - 3. 12A - 106 = 9A - 27. 3A = 79. A = 79/3.

Multiple choice

Anil has taken 50 tests in a school and passed some of them, getting test passing average of 20%. Find the number of more tests that he must pass to attain test passing average of 60%; and he has passed every test after 50 tests.

  1. 30

  2. 40

  3. 50

  4. 60

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

Anil passed 20% of 50 = 10 tests. Let x be the number of additional tests. Total tests = 50 + x. Passed tests = 10 + x. We want (10 + x) / (50 + x) = 0.6. 10 + x = 30 + 0.6x => 0.4x = 20 => x = 50.

Multiple choice

A student scored 30% marks in the first paper of Physics out of 180 marks. He has to get an overall score of 50% in two papers. The second paper is carrying 150 marks. The percentage of marks he should score in the second paper to get the overall average score is:

  1. 80%

  2. 76%

  3. 74%

  4. 70%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total marks = 180 + 150 = 330. Required total = 50% of 330 = 165. Marks in first paper = 30% of 180 = 54. Marks needed in second paper = 165 - 54 = 111. Percentage = (111/150)*100 = 74%.

Multiple choice

The average age of 10 persons is 48 years while that of 8 persons is 47 years. The age of one of the other two persons is 60% more than the other one. The ages of these persons are

  1. 30 years and 48 years

  2. 35 years and 56 years

  3. 40 years and 64 years

  4. 45 years and 72 years

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

Sum of 10 = 480. Sum of 8 = 376. Sum of remaining 2 = 104. Let ages be x and 1.6x. 2.6x = 104, x = 40. The other is 1.6 * 40 = 64.

Multiple choice

The average of fifteen observations is 20. The average of first five observations is 16 and it is 22 for the next seven observations. The thirteenth observation is 2 more than the fourteenth observation, which is 2 more than the fifteenth observation. What is the value of the fifteenth observation?

  1. 7

  2. 15

  3. 20

  4. 25

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

Total sum = 15 * 20 = 300. First 5 sum = 5 * 16 = 80. Next 7 sum = 7 * 22 = 154. Sum of last 3 = 300 - 80 - 154 = 66. Let 15th = x, 14th = x+2, 13th = x+4. x + x+2 + x+4 = 66 => 3x + 6 = 66 => 3x = 60 => x = 20.