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

In a certain packet, there are ten balls of different weight. The weights are denoted by a, b, c, d, e, f, g, h, i, j where 'a' is the lightest ball and the 'j' the heaviest. The average weight of these ten balls is 30. If weight of the lightest ball is not counted, average weight of the remaining 9 balls will be p; and if weight of the heaviest ball is not counted, average weight of the remaining 9 balls will be q. If the sum of p and q is given as 20, what is the average weight of the lightest and the heaviest balls?

  1. 420

  2. 390

  3. 275

  4. 210

  5. 195
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Sum = 300. (Sum - a)/9 = p => Sum - a = 9p. (Sum - j)/9 = q => Sum - j = 9q. Sum - a + Sum - j = 9(p+q) => 600 - (a+j) = 9(20) = 180. a+j = 420. Average = (a+j)/2 = 210.

Multiple choice

The average of four numbers is 27. If the first number is increased by K, the second by (K + 7), the third by (2K + 3) and the fourth is decreased by 2, then the new average of the four numbers will become 32. Find the value of K.

  1. 2

  2. 3

  3. 4

  4. 5

  5. 7
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original sum = 4 * 27 = 108. New sum = 108 + K + (K+7) + (2K+3) - 2 = 108 + 4K + 8 = 116 + 4K. New average = (116 + 4K) / 4 = 29 + K. Given new average = 32, so 29 + K = 32, K = 3.

Multiple choice

The average score of a class of 50 students was calculated to be 64.15. It was later discovered that the score of one student was incorrectly taken to be 39, instead of 75. Find the actual average score of the class.

  1. 64.53

  2. 64.87

  3. 64.95

  4. 65.01

  5. 65.12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The original sum of scores was 50 * 64.15 = 3207.5. The error was subtracting 39 and not adding 75. The correction is (75 - 39) = 36. New sum = 3207.5 + 36 = 3243.5. New average = 3243.5 / 50 = 64.87.

Multiple choice

The average marks per student in a class of 30 students were 45. On rechecking, it was found that marks had been entered wrongly in two cases. After correction, these marks were increased by 24 and 34 in the two cases. The corrected average marks per student would be

  1. 75

  2. 60

  3. 56

  4. 47
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Original sum = 30 * 45 = 1350. Corrected sum = 1350 + 24 + 34 = 1408. Corrected average = 1408 / 30 = 46.93, which rounds to 47.