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 average age of a class of 80 girls was 20 years, the average age of 20 of them was 22 years and that of another 20 was 24 years. Find the average age of the remaining girls. एक कक्षा में 80 लड़कियों की औसत आयु 20 वर्ष थी, उनमें से 20 की औसत आयु 22 वर्ष थी और दूसरे 20 की 24 वर्ष थी । तो शेष बची लड़कियों की औसत आयु क्या है ?

  1. 17 years/वर्ष

  2. 19 years/वर्ष

  3. 21 years/वर्ष

  4. 15 years/वर्ष
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total age of 80 girls = 80 × 20 = 1600 years. First 20 girls: 20 × 22 = 440 years. Next 20 girls: 20 × 24 = 480 years. Remaining 40 girls: 1600 - 440 - 480 = 680 years. Average of remaining = 680/40 = 17 years.

Multiple choice

The average age of a family of 6 members is 25 years. If the age of the youngest member be 5 years, the average age of the family at the birth of the youngest member was?

  1. 18 years

  2. 24 years

  3. 23 years

  4. 22 years

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

Current total age = 6 * 25 = 150 years. Youngest is 5 years, so 5 years ago total age = 150 - (6 * 5) = 120 years. But at that time, the youngest wasn't born, so there were only 5 members. Average = 120/5 = 24 years.

Multiple choice

A company has collected 80% of the amount it needs for a new instrument for the company by receiving an average donation of 400 thousand rupees from the partners. The partner represent________% of the total partners whom the company will ask for the donations. If the company is to collect exactly amount needed for the new instrument, the average donation from the remaining partners Rs._____________thousand.

  1. 50, 100

  2. 50, 80

  3. 80, 100

  4. 20, 120

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

The company collected 80% of needed amount at Rs. 400 per partner, so these partners represent 50% of total partners (since 80% of amount from 50% of partners means each remaining partner must give Rs. 100 to reach 100%). If 50% partners gave 400 each (80% of total), remaining 50% need to give 20% of total at Rs. 100 each.

Multiple choice

Find the correct relationship between given quantities. Quantity I: Average, if 43 years old teacher join in a class of 22 students, whose average age is 20 years. Quantity II: Average, if average age of 5 member’s family was 38 years before 70 years old grandfather’s death and a new baby born in family.

  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
C Correct answer
Explanation

Quantity I: With 22 students averaging 20 years, total age = 440. Adding 43-year teacher gives total 483 for 23 people, so average = 483/23 = 21 years. Quantity II: 5-member family with average 38 means total = 190. After 70-year grandfather dies, total becomes 120 for 4 people. New baby (age 0) makes total 120 for 5 people, average = 120/5 = 24 years. Since 24 > 21, Quantity II is greater.

Multiple choice

Average weight of 8 students is 45 kg. When a student is replaced by a teacher, then the average weight is increased by 4 kg. Calculate the weight of the teacher.

  1. 87 kg

  2. 76 kg

  3. 75 kg

  4. Cannot be determined

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

Total weight of 8 students = 8 × 45 = 360 kg. When one student is replaced by teacher, average becomes 49 kg (45 + 4). New total weight = 8 × 49 = 392 kg. Difference = 392 - 360 = 32 kg = teacher's weight - student's weight. Teacher's weight = 32 + student's weight. Without knowing the student's weight, teacher's exact weight cannot be determined.

Multiple choice

In a class of ________ students, number of girls in the class is 6 more than the number of boys in the class. The average weight of the all the students in the class is 42.25 Kg. Average weight of the boys is __________ Kg and average weight of the girls is 40 Kg. Which of the following option satisfies the given condition?

  1. 50, 42

  2. 40, 45

  3. 60, 45

  4. 46, 42

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

Let boys = b, girls = b+6. Check option C: b=27, g=33, total=60. Total weight = 60 × 42.25 = 2535. Boys' weight = 27 × 45 = 1215. Girls' weight = 33 × 40 = 1320. Sum = 1215 + 1320 = 2535. Correct. Check other options: A (50, 42): b=22, g=28. Boys' weight = 22×42 = 924, girls' weight = 28×40 = 1120. Total weight = 2044, but 50×42.25 = 2112. Incorrect. B (40, 45): b=17, g=23. Total = 2110 vs 40×42.25 = 1690. Incorrect. D (46, 42): b=20, g=26. Total = 2064 vs 46×42.25 = 1943.5. Only C works.

Multiple choice

The average age of 7 members of a family is 24 years. If the youngest member is 4 years old, then what was the average age (in years) of the family including the youngest member at the time of the birth of the youngest member?

  1. 21

  2. 22

  3. 20

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

Currently, the total age of 7 members is 7 × 24 = 168. The youngest is 4, so the other 6 members sum to 168 - 4 = 164. Four years ago (at the youngest's birth), these 6 members were each 4 years younger, so their sum was 164 - 24 = 140. Including the newborn (age 0), the total was 140 for 7 members, giving an average of 140/7 = 20 years.

Multiple choice

In the following questions, two equations Quantity I and Quantity II are given. You have to solve both the equations and give answer. The average marks of three students Anuj, Ankit and Anupam is 470. Anuj and Anupam together got 875 marks and Ankit and Anupam together got 845 marks. Quantity I: The marks of Anuj. Quantity II: The marks of Ankit.

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

Let marks be A (Anuj), K (Ankit), P (Anupam). Average of 3 students = 470, so A+K+P = 470*3 = 1410. Given: A+P = 875 and K+P = 845. From A+P = 875, P = 875 - A. From K+P = 845, K = 845 - P = 845 - (875 - A) = A - 30. Substituting in sum equation: A + (A-30) + (875-A) = 1410. A + A - 30 + 875 - A = 1410. A + 845 = 1410. A = 565 (Anuj's marks). Then K = 565 - 30 = 535 (Ankit's marks). Quantity I (565) > Quantity II (535).

Multiple choice

The average weight of 25 candles is 40 grams. If some candles of weight 50 grams each were removed, then average weight becomes 37.5 grams. How many candles of weight 50 grams each were removed? 25 मोमबत्तियों का औसत वजन 40 ग्राम है । यदि 50 ग्राम वजन की कुछ मोमबत्तियों को हटा दिया गया, तो औसत वजन 37.5 ग्राम हो जाता है । 50 ग्राम वजन की कितनी मोमबत्तियों को हटाया गया?

  1. 3

  2. 5

  3. 8

  4. 12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial total weight = 25 × 40 = 1000g. After removing n candles of 50g each, new total = 1000 - 50n and new count = 25 - n. The new average is 37.5, so (1000 - 50n)/(25 - n) = 37.5. Solving: 1000 - 50n = 937.5 - 37.5n, giving 12.5n = 62.5, so n = 5 candles.

Multiple choice

The average weight of A, B and C is 49 kg. If the average weight of A and B is 35 kg and that of B and C is 62 kg, then the weight of B (in kgs) is? A, B और C का औसत वजन 49 किलोग्राम है। यदि A और B का औसत वजन 35 किलोग्राम है और B और C का औसत 62 किलोग्राम है, तो B ( किलोग्राम में) का वजन क्या है?

  1. 47

  2. 45

  3. 43

  4. 49
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A + B + C = 49 × 3 = 147 kg. A + B = 35 × 2 = 70 kg. B + C = 62 × 2 = 124 kg. From A + B + C = 147 and B + C = 124, we get A = 23 kg. Then B = 70 - 23 = 47 kg.

Multiple choice

Average age of A and B is 24 years and average age of B, C and D is 22 years. The sum of the ages of A, B, C and D is?

  1. 35 years

  2. 40 years

  3. 42 years

  4. Data inadequate

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

Average of A and B = 24, so A + B = 48. Average of B, C, D = 22, so B + C + D = 66. We need A + B + C + D. Adding the two equations: (A + B) + (B + C + D) = 48 + 66 = 114. This gives A + 2B + C + D = 114. But we need A + B + C + D. Without knowing B's individual value, we cannot determine A + B + C + D uniquely. Different values of B would give different sums. Therefore the data is inadequate.

Multiple choice

In a class of 800 students, 56% students are boys. The average weight of all the boys is 75 kg and that of all the girls is 55 kg. Quantity I: What is the average weight of the class? Quantity II: If a boy of 80 kg and a girl of 50 kg is added in the class, then what will be the average weight of the class?

  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 relation can't be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Number of boys = 56% of 800 = 448, number of girls = 352. Total weight = 448×75 + 352×55 = 33600 + 19360 = 52960 kg. Average weight (Quantity I) = 52960/800 = 66.2 kg. After adding one boy (80 kg) and one girl (50 kg), total weight = 52960 + 130 = 53090 kg and total students = 802. New average (Quantity II) = 53090/802 ≈ 66.19 kg. Since 66.2 > 66.19, Quantity I is greater.

Multiple choice

The average marks of 50 students were found to be 40. Later on, it was discovered that a score of 53 was misread as 83. Find the correct average corresponding to the correct score. 50 छात्रों के औसत अंक 40 थे। बाद में पता चला कि एक छात्र के 53 अंकों को गलती से 83 पढ़ लिया गया था। सही अंकों के साथ सही औसत होगा ।

  1. 39.4

  2. 38.9

  3. 38.7

  4. 39
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Original sum = 50 × 40 = 2000. Correct sum = 2000 - 83 + 53 = 1970. Correct average = 1970 ÷ 50 = 39.4. The error was counting 30 extra points (83 - 53), which reduced average by 30/50 = 0.6.

Multiple choice

The average age of 37 boys in a class is 12 years. If the age of their teacher is also included, the average increases by 1.5 year. The teacher's age in years is / एक कक्षा में 37 लड़कों की औसत आयु 12 वर्ष है। यदि उनके शिक्षक की उम्र भी शामिल है, तो औसत 1.5 वर्ष बढ़ जाता है। वर्षों में शिक्षक की आयु है

  1. 60

  2. 79

  3. 69

  4. 54
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total age of 37 boys = 37 × 12 = 444 years. When teacher is included, average becomes 12 + 1.5 = 13.5 years for 38 people, so total = 38 × 13.5 = 513 years. Teacher's age = 513 - 444 = 69 years. Option A (60) would be if you incorrectly used 37 × 1.5 instead of 38 × 13.5.

Multiple choice

A class consists of students whose average weight is 65.5. Four students of 72.2 kg, 70.3 kg, 67.7 kg and 70.8 kg, joined the class and the average weight increased by 500 gms. Find the initial number of students. एक कक्षा में कुछ छात्रों का औसत वजन 65.5 किलोग्राम है । 72.2 किग्रा, 70.3 किग्रा, 67.7 किग्रा और 70.8 किग्रा के चार छात्र कक्षा में शामिल होते है जिससे औसत वजन 500 ग्राम बढ़ गया । छात्रों की प्रारंभिक संख्या ज्ञात कीजिए ।

  1. 16

  2. 20

  3. 24

  4. 34
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let n be the initial number of students. Total initial weight = 65.5n. After 4 students join: total weight = 65.5n + (72.2 + 70.3 + 67.7 + 70.8) = 65.5n + 281. New average = 65.5 + 0.5 = 66. So: (65.5n + 281)/(n+4) = 66. Solving: 65.5n + 281 = 66n + 264, so 17 = 0.5n, giving n = 34.