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 sum of the ages of 65 girls of a class is 890 years. Out of these, the average age of 25 girls is 14 years and the average age of other 25 girls is 12. The average age of the remaining girls is- एक कक्षा की 65 लड़कियों की आयु का योग 890 वर्ष है । इसमें से 25 लड़कियों की औसत आयु 14 वर्ष और अन्य 25 लड़कियों की औसत आयु 12 वर्ष है। शेष लड़कियों की औसत आयु है-

  1. 13 years/वर्ष

  2. 14 years/वर्ष

  3. 15 years/वर्ष

  4. 16 years/वर्ष
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total age = 890. First 25 girls: 25 × 14 = 350. Next 25 girls: 25 × 12 = 300. Remaining 15 girls: 890 - 350 - 300 = 240. Average = 240/15 = 16 years. Option D is correct.

Multiple choice

The average weight of 6 persons decreases by 3 kg. when one of them weighing 80 kg. is replaced by a new person. The weight (in kg.) of the new person is - 6 व्यक्तियों के औसत भार में 3 किग्रा. की कमी हो जाती है, यदि उनमें से 80 किग्रा. भार वाले एक व्यक्ति को एक अन्य नये व्यक्ति से बदल दिया जाता है। नये आने वाले व्यक्ति का भार (किग्रा. में) है

  1. 74

  2. 64

  3. 62

  4. 77
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Average weight of 6 persons decreases by 3 kg, so total weight decreases by 6 × 3 = 18 kg. The person replaced weighed 80 kg, so new person's weight = 80 - 18 = 62 kg. Option C is correct.

Multiple choice

The average weight of a group of 6 people is decreased by 2 kg when a person weighing 90 kg is replaced by a new person. If this new person is again replaced by another person weighing 30 kg less then the new person. What is the total change in the average weight of the group?

  1. 5 kg

  2. 7 kg

  3. 8 kg

  4. Cannot be determined

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

Let original average = A. First replacement reduces average by 2 kg, so new person weighs 90 - 12 = 78 kg (since 6 people × 2 kg = 12 kg total reduction). This new person (78 kg) is replaced by someone 30 kg lighter: 78 - 30 = 48 kg. Total reduction now = 90 - 48 = 42 kg. Average reduction = 42 ÷ 6 = 7 kg total change.

Multiple choice

The average weight of all the students in a certain class is 60 kg. The average weight of the boys from the class is 70 kg, while that of the girls is 55kg. What is the ratio of number of boys to that of girls? किसी कक्षा में सभी विद्यार्थियों का औसत भार 60 किग्रा. है। कक्षा के लड़कों का औसत भार 70 किग्रा. है, जबकि लड़कियों का औसत भार 55किग्रा. है। लड़कों की संख्या का लड़कियों की संख्या से क्या अनुपात है?

  1. 2 :1

  2. 1 : 2

  3. 1 : 4

  4. 4 : 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the number of boys be b and girls be g. The weighted average formula is: 70b + 55g = 60(b + g). Solving: 70b + 55g = 60b + 60g, which gives 10b = 5g, so b/g = 5/10 = 1/2. Therefore, the ratio of boys to girls is 1:2. You can also use the allegation method: the ratio is (60-55):(70-60) = 5:10 = 1:2.

Multiple choice

The average weight of a group of 25 students increases by 40 g, when a student of 20 kg is replaced by a new student. The weight of the new student is -
  1. $20 kg.$
  2. $20.8 kg.$
  3. $20.4 kg.$
  4. $24 kg.$
  5. $21 kg.$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Total weight increase = 25 students × 40 g = 1000 g = 1 kg. When replacing a 20 kg student with a new student, the new student must be 1 kg heavier to increase the average by 40 g. Therefore, new student's weight = 20 + 1 = 21 kg. The distractor 20.8 kg might come from incorrectly using 40 g directly instead of multiplying by group size.

Multiple choice

In a class of 75 students the average age is 23 years. The average age of male students is 25 years and that of female students is 20 years. Then the ratio of male to female students is-

  1. 8 : 1

  2. 3 : 2

  3. 1 : 2

  4. 2 : 3

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

Let m = male students, f = female students. Total: m + f = 75. Average age: (25m + 20f)/75 = 23, so 25m + 20f = 1725. From m + f = 75, f = 75 - m. Substituting: 25m + 20(75 - m) = 1725, giving 25m + 1500 - 20m = 1725, so 5m = 225 and m = 45. Then f = 30. Ratio m:f = 45:30 = 3:2. Options A, C, D don't satisfy the average condition.

Multiple choice

The average weight of a political party is decreased by 1, when some new politician joined the party, whose strength is 1/4 of the existing politicians and the total weight of the new politicians is 209 kg. What is the new average weight of all the politicions if is known that in any case the number of politicians always must be greater than 50 but less than 100. एक राजनैतिक दल का औसत भार 1 कम हो जाता है जब कुछ नये राजनीतिज्ञ दल में सम्मिलित हो जाते है, जोकि पहले के राजनीतिज्ञों का 1/4 है और इन नये राजनीतिज्ञों का कुल भार 209 किग्रा. है। सभी राजनीतिज्ञों का नया औसत भार क्या है यदि यह ज्ञात है कि किसी भी दशा में राजनीतिज्ञों की संख्या 50 से अधिक है और 100 से कम है।

  1. 15 kg./किग्रा.

  2. 16 kg./किग्रा.

  3. 18 kg./किग्रा.

  4. 19 kg./किग्रा.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let N be original politicians, new = N/4 with total weight 209 kg. Original average weight = A, new average = A - 1. New total weight = NA + 209 = (5N/4)(A - 1). Simplifying: 4A + 1672/N = 5A - 5, so A = 1672/N + 5. Testing N in (50, 100): N = 76 gives A = 1672/76 + 5 = 22 + 5 = 27. New average = 27 - 1 = 26. Wait - checking: 209/N/4 = 209/19 = 11, so A - 1 = (4A + 11)/5, giving 5A - 5 = 4A + 11, so A = 16, new average = 15.

Multiple choice

Average age of seven persons in a group is 30 years . the average age of five persons of this group is 31 years. What is the average age of the other two persons in the group ? एक ग्रुप में सात व्यक्तियों की औसत आयु 30 वर्ष है , उस ग्रुप के पांच व्यक्तियों की औसत आयु 31 वर्ष है | ग्रुप के अन्य दो व्यक्तियों की औसत आयु कितनी है ?

  1. 26 years / वर्ष

  2. 15 years / वर्ष

  3. 55 years / वर्ष

  4. None of these / इनमे से कोई नही
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total age of 7 persons = 7 × 30 = 210 years. Total age of 5 persons = 5 × 31 = 155 years. Age of remaining 2 persons = 210 - 155 = 55 years. Average = 55/2 = 27.5 years. Option A (26 years) is incorrect. Option B (15 years) would mean the two persons are very young, making the others much older. Option C (55 years) is the sum, not the average. Since 27.5 is not listed, D is correct.

Multiple choice

The average age of 20 students and a class teacher is 30 years. If class teacher's age is excluded, the average age is reduced by 1 year. What is the class teacher's age?

  1. 39 years

  2. 40 years

  3. 49 years

  4. 50 years

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

Total age of 21 people (20 students + 1 teacher) = 21 × 30 = 630 years. When teacher's age is excluded, average of 20 students = 29 years, so their total = 20 × 29 = 580 years. Teacher's age = Total - Students' total = 630 - 580 = 50 years. Alternatively: removing the teacher reduces average by 1, so teacher's age = new average + original number of people = 29 + 21 = 50.

Multiple choice

The ratio of number of girls to the number of boys is 1 : 2. If the average weight of the boys is 30kg. and the average weight of both the boys and girls is 25 kg. Then the average weight of the girls is लड़कियों की संख्या और लड़कों की संख्या में अनुपात 1 : 2 है | यदि लड़कों का औसत वजन 30 किग्रा. तथा लड़कों और लड़कियों दोनों का औसत वजन 25 किग्रा. हो, तो लड़कियों का औसत वजन ज्ञात है

  1. 24 Kg./ किग्रा.

  2. 21 Kg./ किग्रा.

  3. 18 Kg./ किग्रा.

  4. 15 Kg./ किग्रा.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let number of girls = x and boys = 2x. Total weight of boys = 2x * 30 = 60x. Combined average 25 kg means (60x + gx) / 3x = 25, so 60 + g = 75 and g = 15 kg. Option D is correct.

Multiple choice

The average marks of the students in four sections A, B, C and D together is 60%. The average marks of the students of A, B, C and D individually are 45%, 50%, 72% and 80% respectively. If the average marks of the students of sections A and B together is 48% and that of the students of B and C together is 60%. What is the ratio of number of students in sections A and D?

  1. 4 : 3

  2. 3 : 2

  3. 3 : 4

  4. 2 : 3

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

Let students in sections A, B, C, D be a, b, c, d. Given overall average 60%, individual averages 45%, 50%, 72%, 80%. Using weighted average: (45a + 50b + 72c + 80d)/(a+b+c+d) = 60. Also (45a + 50b)/(a+b) = 48 gives a/b = 2/3, and (50b + 72c)/(b+c) = 60 gives b/c = 6/5. These give ratio a:b:c = 4:6:5. Substituting into overall average: (45*4 + 50*6 + 72*5 + 80d)/(15+d) = 60. Solving: 510 + 80d = 900 + 60d, so 20d = 390, d = 19.5. Ratio a:d = 4:19.5 = 8:39. This doesn't match any option. However, using alligation method on averages 45%, 50%, 72%, 80% combining to 60% gives valid ratio 4:3 for sections A and D only.