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

A group of four persons consist of two men A and B, and two women C and D. The average weight of all four is 55 kg. The average weight of the two men is over 60 kg. D weighs more than 52 kg. In this context, which one of the following statements follows logically?

  1. Any man weighs more than any woman.

  2. C's weight is less than 49 kg.

  3. C's weight is the lowest

  4. Either of the men weighs more than 60 kg.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total weight of all four = 4 × 55 = 220 kg. Since D > 52 kg, A + B + C < 220 - 52 = 168 kg. The two men (A and B) average over 60 kg, so A + B > 120 kg. Therefore C < 168 - 120 = 48 kg. This means C weighs less than 48 kg. Since both men average over 60 kg and D > 52 kg, C must be the lightest person in the group.

Multiple choice

The average of 17 numbers is 45. The average of the first 9 numbers is 51 and that of the last 9 numbers is 36. Find the 9th number.

  1. 14

  2. 20

  3. 18

  4. 22
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Sum of all 17 numbers = 17×45 = 765. Sum of first 9 numbers = 9×51 = 459. Sum of last 9 numbers = 9×36 = 324. When we add the sums of first 9 and last 9, the 9th number is counted twice. So 459+324-9th number = 765, giving 783-9th number = 765, so 9th number = 18.

Multiple choice

The average weight of 15 girls was recorded as 54 kg. If the weight of the teacher was added, the average increased by two kg. What was the teacher's weight?

  1. 75 kg

  2. 95 kg

  3. 78 kg

  4. 86 kg
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total weight of 15 girls = 15 × 54 = 810 kg. With teacher, total weight = 16 × 56 = 896 kg (average increases by 2 kg). Teacher's weight = 896 - 810 = 86 kg. Option A (75 kg) assumes adding only 21 kg, which doesn't change the average correctly.

Multiple choice

The average of 8 persons is increased by 2 years ,when one of them whose age is 24 years is replaced by a new person. The age of the new person is -

  1. 42 years

  2. 40 years

  3. 38 yeas

  4. 45 years
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When replacing a person in a group, if the average increases by 2, the new person must be 2 × 8 = 16 years older than the person they replaced. Since the replaced person was 24 years old, the new person is 24 + 16 = 40 years old. Note: option C has a typo ('yeas' instead of 'years').

Multiple choice

12 persons went a hotel for taking their meals. 11 of them spent Rs 150 each over their meals and the 12th spent Rs 22 more than the average expenditure of all . What is the amount that 12th has spent on his food?

  1. Rs 155

  2. Rs 151

  3. Rs 154

  4. Rs 152

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

Let the average expenditure be A. Then 11 persons spent 150 each, and 12th person spent A + 22. So 11 × 150 + (A + 22) = 12A. This gives 1650 + A + 22 = 12A, so 1672 = 11A, and A = 152. The 12th person spent 152 + 22 = 174, which is not among the given options, so the answer is None of these.

Multiple choice

Find the correct relationship between the given quantities: Quantity I: The present average weight of 15 students of a class, if earlier, the average weight of 14 students, each weighing 1.5 kg more then the present weight, was 56kg and now a new boy weighing 50 kg was added as the 15th student. Quantity II: The number of ways 3 people from 3 men and 3 women can be selected and arranged on 3 chairs such that atmost one of them is a woman.

  1. Quantity II > Quantity I

  2. Quantity I ≥ Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or relationship cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: If 14 students had average weight of 56 kg when each weighed 1.5 kg more, then their present average weight = 56 - 1.5 = 54.5 kg. Adding a 15th student weighing 50 kg, new average = (14×54.5 + 50)/15 = (763 + 50)/15 = 813/15 = 54.2 kg. Quantity II: Selecting and arranging 3 people from 3 men and 3 women with at most one woman. Cases: 0 women (3 men): 3P₃ = 6 ways. 1 woman (2 men): C(3,1) × C(3,2) × 3! = 3 × 3 × 6 = 54 ways. Total = 60 ways. Since 60 > 54.2, Quantity II > Quantity I.

Multiple choice

There are 100 students in 3 sections A, B and C of a class. The average marks of all the 3 sections was 84. The average of B and C was 87.5 and the average marks of A is 70. The number of students in A was-

  1. 30

  2. 35

  3. 20

  4. 25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let students in A = x, then students in B + C = 100 - x. Total marks = 100 × 84 = 8400. Section A marks = 70x. Combined marks of B and C = 87.5(100 - x) = 8750 - 87.5x. So: 70x + (8750 - 87.5x) = 8400. Solving: -17.5x = -350, so x = 20. This is a weighted average problem where section A has lower average than B and C combined.

Multiple choice

In an exam, the average marks obtained by the students was found to be 60. After omission of computational errors, the average marks of 100 candidates had to be changed from 60 to 30 and the average with respect to all the examinees came down to 45 marks. The total number of candidates who took the exam, was एक परीक्षा में, छात्रों के द्वारा प्राप्त औसत अंक 60 पाए गए | संभावित त्रुटि को हटाने के बाद, 100 अभ्यर्थियों का औसत परिवर्तित होकर 60 से 30 हो गया और सभी परीक्षार्थियों के सापेक्ष औसत घटकर 45 अंक हो गया | कुल अभ्यर्थियों की संख्या जिन्होंने परीक्षा दी, थी

  1. 200

  2. 210

  3. 240

  4. 180
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using alligation method: 100 students with average 30 are mixed with (n-100) students with average 60 to get overall average 45. The ratio is (60-45) : (45-30) = 15 : 15 = 1 : 1. So n-100 = 100, giving n = 200. Alternative: (100×30 + (n-100)×60)/n = 45 gives same result.

Multiple choice

The average weight of a political party is decreased by 1, when some new politician joined the party whose strength is (\frac{1}{4}) of the existing politicians and the total weight of the new politicians is 209 kg. What is the average weight the politicians joined if is known that in any case the number of politicians always must be greater than 50 but less than 100.

  1. 11

  2. 19

  3. 15

  4. 16

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

Let x be original politicians, so x/4 new politicians joined. Total weight of new politicians is 209 kg, so their average is 209 ÷ (x/4) = 836/x. The average decreases by 1: (total weight + 209)/(x + x/4) = original average - 1. If original average is A, then (xA + 209)/(5x/4) = A - 1. Solving gives A - 836/x = 1, so A = (836/x) + 1. New politician average = 836/x = A - 1. The politicians joined reduces average, so their average < original average. This means 836/x < (836/x) + 1, which is always true. Given 50 < x + x/4 < 100 (must be > 50 and < 100), x must be divisible by 4. Options: 40 (fails), 44 (fails), 48 (55 total, works), 52 (65 total, works), 56 (70 total, works), 60 (75 total, works), 64 (80 total, works), 68 (85 total, works), 72 (90 total, works), 76 (95 total, works), 80 (100 total, fails). Checking new average = 836/x: For x=48, avg=17.42; for x=52, avg=16.08; for x=56, avg=14.93; for x=60, avg=13.93; for x=64, avg=13.06; for x=68, avg=12.29; for x=72, avg=11.61; for x=76, avg=11. So x=76 gives average = 11, which matches option A.

Multiple choice

Each question below contains a statement followed by Quantity I and Quantity II. Find the correct relationship among them. There are 84 students in a class whose average age is 13 years. The average age of the girls in the class is 15 years while the average age of the boys is 12 years? Quantity I: No of boys in the class is? Quantity II: No of girls in the class is?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let b = boys, g = girls. Total: b + g = 84. Weighted age: 12b + 15g = 13 × 84 = 1092. Solving gives b = 52, g = 32. Quantity I (boys = 52) > Quantity II (girls = 32). The answer comes from solving the two equations.

Multiple choice

Find the correct relationship between Quantity I and Quantity II. \ Quantity I: The age of teacher, if the average age of 36 students is 14. When teacher’s age is included the average increases by 1. \ Quantity II: The age of professor if the average age of 19 students is 35. When professor’s age is included the average increases by 0.5.

  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 relationship cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: With 36 students averaging 14 years, total = 504. When teacher joins, 37 people average 15 years, total = 555. Teacher's age = 555 - 504 = 51 years. Quantity II: With 19 students averaging 35 years, total = 665. When professor joins, 20 people average 35.5 years, total = 710. Professor's age = 710 - 665 = 45 years. Since 51 > 45, Quantity I > Quantity II.

Multiple choice

The average weight of 5 persons sitting in a boat is 38 kg. The average weight of the boat and the persons sitting in a boat is 52 kg. What is the weight of the boat?
  1. $228 kg.$
  2. $122 kg.$
  3. $232 kg.$
  4. $242 kg.$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total weight of 5 persons = 5 × 38 = 190 kg. Total weight of boat + 5 persons = 6 × 52 = 312 kg (since boat + 5 persons = 6 entities). Therefore, boat weight = 312 - 190 = 122 kg. Option A (228 kg) would be the result of incorrectly adding instead of subtracting. Options C and D are calculation errors.