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

Directions: In the following question, we have two quantities given. Compare these quantities and answer accordingly with the following given options. (a) Quantity I > Quantity II (b) Quantity I < Quantity II (c) Quantity I ≥ Quantity II (d) Quantity I ≤ Quantity II (e) Quantity I = Quantity II or No relation Quantity I: The average weight of A and B is 50 kg, average weight of B and C is 45 kg and average weight of C and A is 55 kg. The weight of A. Quantity II: 45 kg

  1. a

  2. b

  3. c

  4. d

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

(A+B)/2 = 50 -> A+B = 100. (B+C)/2 = 45 -> B+C = 90. (C+A)/2 = 55 -> C+A = 110. Adding these: 2(A+B+C) = 300 -> A+B+C = 150. A = 150 - (B+C) = 150 - 90 = 60. Quantity I (60) > Quantity II (45).

Multiple choice

Directions: In the following question, two quantities are given. Compare these quantities and choose the correct option accordingly. The owner of a company buys an oil at Rs. 10, 12, 15 and 20 per litre for 4 successive years. She spends Rs. 5000 each year. Quantity I: The average cost per litre of oil (approximately) Quantity II: The average cost of oil per litre for the given 4 years

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≤ Quantity II

  4. Quantity I ≥ Quantity II

  5. Quantity I = Quantity II or No relation
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

The average body weights of 4 men A, B, C and D is 50 kg. Decide whether the data given in the statements I, II and III is sufficient to find the individual body weights of B and D. I. The weight of A is 65 kg and that of C is 45 kg. II. The sum of the weights of B and D is 90 kg. III. D has the least weight compared to A, B and C.

  1. Data in I and II is sufficient.

  2. Data in II and III is sufficient.

  3. Data in I, II and III sufficient.

  4. Data in I, II and III is not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Average of 4 = 50, so sum = 200. A+B+C+D = 200. I: A=65, C=45. B+D = 200 - 65 - 45 = 90. II: B+D = 90. III: D is least. Even with all, we only know B+D=90 and D is smaller than A, B, C, but we cannot isolate B or D individually.

Multiple choice

25 persons were sitting in a boat. Their average weight increased one kilogram when one man leaves and a new man comes in. The weight of the new man is 70 kgs. Find the weight of the man who left.

  1. 45 kgs

  2. 52 kgs

  3. 48 kgs

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

Let the total weight be W. When one man (x) leaves and another (70) enters, the new total is W - x + 70. The new average is (W - x + 70)/25 = W/25 + 1. This simplifies to -x + 70 = 25, so x = 45.

Multiple choice

The average weight of 5 boys is 50 kg. If 3 more boys, whose average weight is equal to the weight of the heaviest among the first five boys, join the group, the overall average increases by 3. How much does the heaviest boy among the first five weigh?

  1. 52 kg

  2. 54 kg

  3. 56 kg

  4. 58 kg

  5. 60 kg
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Weighted average: (1/5)(7/8) + (7/20)(1/4) + (2/5)(1/2) + (1/20)(1/2) = 7/40 + 7/80 + 1/5 + 1/40 = (14+7+16+2)/80 = 39/80. 39/80 * M = 172. M = 172 * 80 / 39 = 352.82.

Multiple choice

In a class, average height of all students is 'a' cms. Among them, average height of 10 students is 'b' cms and the average height of the remaining students is 'c' cms. Find the number of students in the class. (Here a > c and b > c)

  1. [a(b - c)](a - c)

  2. (b - c)/(a - c)

  3. (b - c)/[10(a - c)]

  4. [10(b - c)]/(a - c)
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let N be the total students. The sum of heights is a*N. We are given 10*b + (N-10)*c = a*N. Rearranging gives N(a-c) = 10(b-c), so N = 10(b-c)/(a-c).

Multiple choice

The average of some natural numbers is 15. If 30 is added to first number and 5 is subtracted from the last number, the average become 17.5. then the numbers of natural numbers is : কিছু বাস্তব সংখ্যার গড় 15,যদি প্রথম সংখ্যার সাথে 30 যোগ করা হয় এবং শেষ সংখ্যা থেকে 5 বিয়োগ করা হয় তাহলে গড় দাঁড়ায় 17.5, কতগুলি সংখ্যা ছিল?

  1. 12

  2. 15

  3. 10

  4. 11
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let there be n numbers. Their original sum is 15n, and the changed sum is 15n + 30 - 5 = 15n + 25. Since the new average is 17.5, 15n + 25 = 17.5n, giving n = 10.

Multiple choice

A student obtained 60, 75 and 85 marks in three monthly examinations and 95 marks in the final examination in Physics. The three monthly examinations are of equal weightage, whereas the final examination is weighted twice as much as a monthly examination. What are the average marks obtained by the student?

  1. 85

  2. 78

  3. 82

  4. 79

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

Total marks = 60 + 75 + 85 + (95 * 2) = 220 + 190 = 410. Total weight = 1 + 1 + 1 + 2 = 5. Average = 410 / 5 = 82.