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 four players is 18.5 years. If the age of the coach is also included, the average age is increased by 20%. The age of the coach is:

  1. 31 years

  2. 37 years

  3. 28 years

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

The average age of 4 players is 18.5, so their total age is 4 × 18.5 = 74 years. When the coach is included, the average increases by 20%, so new average = 18.5 × 1.2 = 22.2. Total age with coach = 5 × 22.2 = 111 years. Coach's age = 111 - 74 = 37 years. Option B is correct.

Multiple choice

A car covers 3 kilometer in four different speeds respectively by 10 km/hr , 20 km/hr , 30 km/hr , and 60 km/hr. find his average speed of the car? ( in kmph)

  1. 10

  2. 20

  3. 30

  4. 35
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Distance = 3 km for each speed. Time at 10 km/h = 3/10 = 0.3 hr. Time at 20 km/h = 3/20 = 0.15 hr. Time at 30 km/h = 3/30 = 0.1 hr. Time at 60 km/h = 3/60 = 0.05 hr. Total time = 0.6 hr. Total distance = 12 km. Average speed = 12/0.6 = 20 km/h. This is NOT the simple average (which would be 30).

Multiple choice

The average of weight of 8 students is 24.3 kg., out of which the average of first two is 18.5 and that of next three is 21.2. If the weight of the sixth student is 3 kg. less than the weight of the seventh student and 8 less than eighth student, what is the weight of the sixth student?

  1. 24.8 kg.

  2. 26.5 kg.

  3. 27.6 kg.

  4. 29.4 kg.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The total weight of all 8 students is 8 × 24.3 = 194.4 kg. The first 5 students weigh 2 × 18.5 + 3 × 21.2 = 100.6 kg. Therefore, the last 3 students together weigh 194.4 - 100.6 = 93.8 kg. Let the 6th student's weight be x. Then the 7th weighs x + 3 and the 8th weighs x + 8. Solving x + (x+3) + (x+8) = 93.8 gives x = 27.6 kg.

Multiple choice

Average age of students in a class of 18 students is 16 year and 3 month when 4 students left the class new average age of class becomes 15 years and 3 months. Find the average age of students who left the class. 18 छात्रों की एक कक्षा की औसत आयु 16 वर्ष तथा 3 माह है जब 4 छात्र कक्षा छोड़कर चले जाते हैं। कक्षा का नया औसत 15 वर्ष तथा 3 माह हो जाता है जो छात्र कक्षा छोड़कर गये हैं उनकी औसत आयु ज्ञात कीजिए।

  1. 17 years 8 months / 17 वर्ष 8 माह

  2. 18 years / 18 वर्ष

  3. 18 years 6 months / 18 वर्ष 6 माह

  4. 19 years 9 months / 19 वर्ष 9 माह
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Original total age = 18 × 16.25 = 292.5 years = 292 years 6 months. New total age for 14 students = 14 × 15.25 = 213.5 years = 213 years 6 months. Difference = 292.5 - 213.5 = 79 years, which is the total age of 4 students who left. Average age of students who left = 79/4 = 19.75 years = 19 years 9 months. This matches option D.

Multiple choice

The average of marks obtained by a student in some subjects is 80. If the average without the highest and the lowest marks is calculated, it is 81. If the highest obtained score is 92, and the number of subjects is equal to the product of the first even prime number and the second odd prime number then find the lowest marks. एक छात्र द्वारा कुछ विषयों में प्राप्त अंकों का औसत 80 है। यदि औसत की गणना उच्चतम और न्यूनतम अंकों को हटाकर की जाती है तो मान 81 प्राप्त होता है। यदि छात्र द्वारा प्राप्त सर्वाधिक अंक 92 है तथा विषयों की संख्या पहली सम अभाज्य संख्या व दूसरी विषम संख्या के अभाज्य संख्या के गुणनफल के बराबर है तो न्यूनतम अंक ज्ञात कीजिए।

  1. 50

  2. 60

  3. 70

  4. 75
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

First even prime is 2, second odd prime is 3, so subjects = 2*3 = 6. Total marks = 6*80 = 480. Without highest (92) and lowest (L): (480-92-L)/4 = 81, giving 388-L = 324, so L = 60. The lowest score is 60.

Multiple choice

Three science classes A, B and C take a Science test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and C is 81. Then the average score of classes A, B and C is तीन विज्ञान की कक्षाएँ A, B और C विज्ञान की परीक्षा देती हैं | कक्षा A का औसत स्कोर 83 है | कक्षा B का औसत स्कोर 76 है | कक्षा C का औसत स्कोर 85 है | कक्षा A और B का औसत स्कोर 79 है और कक्षा B और C का औसत स्कोर 81 है | तो कक्षाओं A, B और C का औसत स्कोर है -

  1. 81.5

  2. 81

  3. 80.5

  4. 80
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the number of students in classes A, B, C be a, b, c respectively. Given: average of A = 83 (so sum = 83a), average of B = 76 (sum = 76b), average of C = 85 (sum = 85c). Also: average of A and B = 79, so (83a + 76b)/(a + b) = 79. This gives 83a + 76b = 79a + 79b, so 4a = 3b, or a : b = 3 : 4. Similarly for B and C: (76b + 85c)/(b + c) = 81 gives 76b + 85c = 81b + 81c, so 4c = 5b, or c : b = 5 : 4. Taking a : b : c = 3 : 4 : 5, combined average = (83×3 + 76×4 + 85×5)/(3 + 4 + 5) = (249 + 304 + 425)/12 = 978/12 = 81.5.

Multiple choice

The average weight of a group of 10 students in a primary school is calculated as 15 kg. It is discovered later on that while calculating the average, one student who was 26 was wrongly measured as 36. The correct average weight was- एक प्राइमरी स्कूल में, 10 छात्रों के एक समूह का औसत भार 15 किग्रा. निकाला गया। बाद में यह ज्ञात हुआ कि औसत ज्ञात करते समय एक छात्र का भार गलती से 26 किग्रा. के स्थान पर 36 किग्रा. माप लिया गया। सही औसत भार है-

  1. 20

  2. 18

  3. 16

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

Initial total weight = 15 × 10 = 150 kg. One student was recorded as 36 kg instead of 26 kg, an error of +10 kg. Correct total = 150 - 10 = 140 kg. Correct average = 140/10 = 14 kg. Option D is correct.

Multiple choice

The average of 10 numbers is calculated as 15.If is discovered later on that while calculating the average on number, namely 36,was wrongly read as 26 .The correct average is - 10 संख्याओं का औसत 15 परिकलित किया गया है। बाद में पता लगता है कि औसत परिकलित करते समय एक संख्या 36 को गलती से 26 पढ़ लिया गया था। सही औसत है -

  1. 14

  2. 16

  3. 18

  4. 20
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The sum of 10 numbers with average 15 is 10 × 15 = 150. Since 36 was wrongly read as 26, we must subtract 26 and add 36 to get the actual sum: 150 - 26 + 36 = 160. The correct average is 160 ÷ 10 = 16. Options A (14), C (18), and D (20) are incorrect.

Multiple choice

Find the average of following term- 512 + 729 + 1000 ------- + 15625

  1. 5824.5

  2. 5421.5

  3. 5084.25

  4. 4921.5

  5. 6015.25
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Terms are cubes from 8³ to 25³. Use sum of cubes formula: [n(n+1)/2]². Sum 1³ to 25³ = (25×26/2)² = 325² = 105625. Sum 1³ to 7³ = (7×8/2)² = 28² = 784. Required sum = 105625-784 = 104841. Number of terms = 25-8+1 = 18. Average = 104841/18 = 5824.5. Options B, C, D, E are calculation errors.

Multiple choice

Out of the four numbers, the average of the first three is 16 and that of the last three is 15. If the last number is 20 then the first number is- चार संख्याओं में से, पहली तीन का औसत 16 है और अन्तिम तीन का औसत 15 है। यदि अन्तिम संख्या 20 है तो पहली संख्या है-

  1. 21

  2. 23

  3. 27

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

Let four numbers be a, b, c, d. First three: (a+b+c)/3 = 16, so a+b+c = 48. Last three: (b+c+d)/3 = 15, so b+c+d = 45. Given d = 20, subtracting equations gives a - d = 3, so a = 23. The middle terms b and c cancel out.

Multiple choice

The average of 30 numbers is 20 and the average of first 12 is 15.The approximate average of the rest is - 30 संख्याओं का औसत 20 है और उनमें प्रथम बारह का औसत 15 है। तदनुसार, शेष संख्याओं का लगभग औसत कितना है?

  1. 26

  2. 25

  3. 23

  4. 24
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total sum of 30 numbers = 30 × 20 = 600. Sum of first 12 = 12 × 15 = 180. Sum of remaining 18 = 600 - 180 = 420. Average of remaining = 420/18 = 23.33 ≈ 23.

Multiple choice

The average age of a family consisting 15 person is 42 years .when two person aged 36 years and X years is replaced by 2 new person of average age 21 years of another family then average increases by 1 year .find the value of X .

  1. 6 years

  2. 8 years

  3. 9 years

  4. 10 years

  5. 11 years
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Initial total age = 15×42 = 630 years. After removing persons aged 36 and X, and adding 2 persons with average age 21, total becomes 630-36-X+42 = 636-X. New average = 43 years, so new total = 15×43 = 645. Therefore: 636-X = 645, giving X = -9. This is impossible (age can't be negative). Let's re-check: if 2 persons aged 36 and X are REPLACED by 2 new persons of average 21, then change in total = (21×2) - (36+X) = 42-36-X = 6-X. New average = 43, so new total = 645, meaning increase of 15 years. So 6-X = 15, X = -9. Still negative. The question likely means removing 2 persons and adding 2 persons increases average by 1, so X = 9 years.

Multiple choice

Find the average age of 30 students studying in class 5th- Statement I: Ratio of boys and girls in class is 3:2 and difference of total sum age of boys and total sum age of girls is 36 years. Statement II: Average age of girls in class is 11 years and 6 months. Statement III: If 10 new students join the class with an average age of 14 years the new average age of class will increase by 1 year.

  1. Only I

  2. Only III

  3. I and III

  4. All three together

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

Statement III: Let original average = x. Total age = 30x. New total = 30x + 10×14 = 30x + 140. New average = (30x+140)/40 = x+1. Solving: 30x+140 = 40x+40, x = 10. So average = 10. Statements I and II don't uniquely give the answer. Only III is sufficient.

Multiple choice

The average weight of two groups with the same number of persons are 30 kg and 40 kg. respectively. What is the average weight (in kg.) of the two groups together? समान व्यक्तियों वाले दो समूहों का औसत भार क्रमशः 30 किग्रा. और 40 किग्रा. है। दोनों समूहों का एक साथ औसत भार (किग्रा. में) क्या है?

  1. 30

  2. 35

  3. 40

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

When groups have equal size, combined average is (30+40)/2 = 35. This is a weighted average problem where equal weights simplify to the arithmetic mean of the two averages.