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 pair of 6 numbers, the average of the first four numbers is 10 and the average of the last four numbers is 8. If the average of all 6 numbers is 9, find the average of the third and fourth numbers.

  1. 7

  2. 8

  3. 9

  4. 10

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

Let 6 numbers be a,b,c,d,e,f. Given: (a+b+c+d)/4=10 so a+b+c+d=40. (c+d+e+f)/4=8 so c+d+e+f=32. Total average 9 means sum=54. Adding first two equations: a+b+2c+d+e+f=72. Subtracting total: (a+b+2c+d+e+f)-(a+b+c+d+e+f)=72-54, giving c+d=18. Average of c,d = 18/2=9.

Multiple choice

Three seminars were conducted on healthy eating, lifestyle and stress. The ratio of number of attendees in each seminar was 7:9:8 and it was known that a person attends either one or all three seminars. If 144 people from a total of 1392 people attending the seminars, came to all 3 of them. Considering the people that attended one seminar only, what is the average number of people that went for healthy eating or lifestyle? सेहतपूर्ण भोजन, जीवनशैली और तनाव पर तीन सेमिनार आयोजित किये गये। प्रत्‍येक सेमिनार में भाग लेने वाले लोगों की संख्‍या में अनुपात 7:9:8 था और यह ज्ञात था कि कोई व्‍यक्ति या तो एक अथवा तीनों सेमिनारों में भाग लेता है। यदि कुल 1392 लोगों में से 144 लोगों ने तीनों सेमिनार में हिस्‍सा लिया हो, तो केवल एक सेमिनार में भाग लेने वाले लोगों की संख्‍या को ध्‍यान में रखकर बेहतर भोजन अथवा जीवनशैली के लिये जाने वाले लोगों की औसत संख्‍या क्‍या है?

  1. 320

  2. 160

  3. 480

  4. 288

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

Total ratio units: 7+9+8 = 24. Total people: 1392. Each unit = 1392/24 = 58. Healthy eating: 7×58 = 406, Lifestyle: 9×58 = 522, Stress: 8×58 = 464. People attending only one seminar = 1392 - 144 = 1248 (subtracting those who attended all 3). Only healthy: 406-144 = 262, Only lifestyle: 522-144 = 378. Average of these = (262+378)/2 = 320.

Multiple choice

The average age of 160 boys in a class is 15 years. The average age of a group of 30 boys in the class is 16 years and the average age of another 50 boys in the class is 14 years. What is the average age of the remaining boys in the class? एक कक्षा में 160 लड़कों की औसत आयु 15 वर्ष है। कक्षा में 30 लड़कों के समूह की औसत आयु 16 वर्ष है और कक्षा में अन्य 50 लड़कों की औसत आयु 14 वर्ष है। कक्षा में शेष लड़कों की औसत आयु क्या है?

  1. 15.25

  2. 15.50

  3. 15

  4. 16.25

  5. None of these इनमे से कोई नही|
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total age of 160 boys = 160×15 = 2400 years. Age of first 30 boys = 30×16 = 480 years. Age of next 50 boys = 50×14 = 700 years. Remaining boys = 160-30-50 = 80. Their total age = 2400-480-700 = 1220 years. Average age = 1220/80 = 15.25 years. Option A is correct.

Multiple choice

Average weight of a group of 15 members is increased by 850 grams when a new person of weight 72 Kg joined the group. Find the sum of weight of all members in group earlier. 15 सदस्यों के समूह का औसत वजन 850 ग्राम बढ़ जाता है जब 72 किलोग्राम वजन का एक नया व्यक्ति समूह में शामिल हो जाता है। पहले समूह में सभी सदस्यों के वजन का योग ज्ञात कीजिए।

  1. 875

  2. 752

  3. 899

  4. 795

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

Let initial average weight be A kg for 15 members. Total weight = 15A. When new person joins: (15A + 72)/16 = A + 0.85. Solving: 15A + 72 = 16A + 13.6, giving A = 58.4 kg. Initial total weight = 15 × 58.4 = 876 kg. None of 875, 752, 899, or 795 match.

Multiple choice

The question given below is followed by some statements. Read the question carefully and statements and determine which of the given statements is/are necessary/required to answer the question. नीचे दिए गए प्रश्न के बाद कुछ कथन दिए गए हैं। प्रश्न को ध्यान से पढ़ें और निर्धारित करें कि दिए गए कथनों में से कौन सा / से प्रश्न का उत्तर देने के लिए आवश्यक / आवश्यक है /हैं । What is the average weight of boys in the class? कक्षा में लड़कों का औसत वजन कितना है? I. Average weight of all the 60 students is 45 kg. II. Average weight of girls is 50 kg. III. Total weight of all the boys together is 1250 kg. I. सभी 60 छात्रों का औसत वजन 45 किलोग्राम है। II. लड़कियों का औसत वजन 50 किलोग्राम है। III. एक साथ सभी लड़कों का कुल वजन 1250 किलोग्राम है।

  1. Only II and III

  2. I and either II or III

  3. Any two of these

  4. All I, II and III

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let number of boys = b, girls = g. Total students = 60. From I: Total weight = 60×45 = 2700 kg. From II: Girls' average = 50 kg, so total girls' weight = 50g. From III: Total boys' weight = 1250 kg. Average boys' weight = 1250/b. We need b to find this average. Using I and II: 2700 = 1250 + 50g, so 50g = 1450, g = 29. Then b = 60-29 = 31. Boys' average = 1250/31 ≈ 40.32 kg. All three statements are necessary - I gives total, II gives girls' average to find g, III gives boys' total weight.

Multiple choice

Find the value of both quantities and state the correct relationship. दोनों मात्राओं का मान ज्ञात कीजिये और सही संबंध स्थापित कीजिये। Quantity I: Marks of new student, if the average marks of 25 students is 55 and after the marks of new student also taken into consideration, average increases by 2 marks Quantity II: Marks of new student, if the average marks of 20 students is 80 and after the marks of new student also taken into consideration, average increases by 1.5 marks मात्रा I: नए छात्र के अंक, यदि 25 छात्रों के औसत अंक 55 हैं और और यदि नए छात्र के अंक भी सम्मिलित किये जाते हैं, तो औसत 2 अंक बढ़ जाता है। मात्रा II: नए छात्र के अंक, यदि 20 छात्रों के औसत अंक 80 हैं और यदि नए छात्र के अंक भी सम्मिलित किये जाते हैं, तो औसत 1.5 अंक बढ़ जाता है।

  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity II > Quantity I मात्रा II > मात्रा I

  4. Quantity II Quantity I मात्रा II मात्रा I

  5. Quantity I = Quantity II or Relation cannot be established मात्रा I = मात्रा II या संबंध स्थापित नहीं किया जा सकता है
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Total marks = 25×55 + x = 1375 + x, New average = (1375+x)/26 = 57, so x = 1482-1375 = 107. Quantity II: Total marks = 20×80 + y = 1600 + y, New average = (1600+y)/21 = 81.5, so y = 1711.5-1600 = 111.5. Quantity II (111.5) > Quantity I (107). The claimed answer is correct.

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. मात्रा I: एक कक्षा में वर्तमान में 15 छात्रों का औसत भार, यदि पहले, 14 छात्रों का औसत भार, वर्तमान भार से प्रत्येक के भार से 1.5 कि.ग्रा. अधिक, 56 किग्रा था और नया लड़का जिसका वज़न 50 कि.ग्रा है को 15वें छात्र के रूप में जोड़ा गया। मात्रा II: तरीकों की संख्‍या जिसे 3 आदमी और 3 औरतों में से 3 लोगों द्वारा चुना जा सकता है और इन 3 कुर्सियों में से अधिकतम पर एक औरत है।

  1. Quantity II > Quantity I मात्रा II > मात्रा I

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity I > Quantity II मात्रा I > मात्रा II

  4. Quantity I ≤ Quantity II मात्रा I ≤ मात्रा II

  5. Quantity I = Quantity II or relationship cannot be established मात्रा I = मात्रा II या कोई संबंध स्थापित नहीं किया जा सकता
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: 14 students at 56 kg average were each 1.5 kg heavier than present. Current weight of these 14 students: (56 - 1.5) × 14 = 54.5 × 14 = 763 kg. Adding 50 kg boy: 763 + 50 = 813 kg. Present average: 813 ÷ 15 = 54.2 kg. Quantity II: Select 3 people from 3 men and 3 women with at most 1 woman. Cases: (i) All 3 men: 3C3 = 1 way, (ii) 2 men + 1 woman: 3C2 × 3C1 = 3 × 3 = 9 ways. Total selection: 10 ways. Arrangement on 3 chairs: 10 × 3! = 10 × 6 = 60 ways. Quantity II (60) > Quantity I (54.2).

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 . किसी परिवार के 15 व्यक्तियों की औसत आयु 42 वर्ष है | जब दो व्यक्ति जिनकी आयु 36 वर्ष और X वर्ष है ,को दूसरे परिवार के 21 वर्ष औसत आयु वाले 2 नए व्यक्तिओं से विस्थापित किया जाता है | तो उस परिवार की औसत आयु 1 वर्ष बढ़ जाती है | X का मान ज्ञात कीजिए |

  1. 13

  2. 11

  3. 7

  4. 9

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

Original sum = 15 × 42 = 630 years. After replacing two people aged 36 and X with two people averaging 21 years, the new sum = 630 - 36 - X + 42 = 636 + X. New average = (636 + X)/15 = 43. Solving: 636 + X = 645, so X = 9. The average increases by 1 year as stated.

Multiple choice

Average weight of a group of 15 members is increased by 850 grams when a new person of weight 72 Kg joined the group. Find the sum of weight of all members in group earlier.

  1. 875

  2. 752

  3. 899

  4. 795

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

Let original average = x kg. Original total = 15x. New total = 15x + 72. New average = (15x + 72) / 16 = x + 0.85. Solving: 15x + 72 = 16x + 13.6, which gives x = 58.4. Original sum = 15 × 58.4 = 876 kg. None of the given options (875, 752, 899, 795) match 876.

Multiple choice

In an office, the average weight of male is 45 and that of the total is 5 less than that of male. If the number of female is one-third less than that of male, find the average weight of female.

  1. 30

  2. 22.5

  3. 35.5

  4. 32.5

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

Male average = 45 kg. Total average = 45 - 5 = 40 kg. Females are one-third less than males, so if males = 3x, females = 2x. Total people = 5x. Total weight = 5x × 40 = 200x. Male weight = 3x × 45 = 135x. Female weight = 200x - 135x = 65x. Female average = 65x / 2x = 32.5 kg.