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 group of some persons is 16.75 years. By joining 20 new persons with an average age of 13.25 years, the average age of the group becomes 15 years. Find out the number of persons in the group initially.

  1. 29

  2. 20

  3. 28

  4. 32

  5. 26
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let initial persons be x with average 16.75, so sum = 16.75x. After 20 persons with average 13.25 join, total persons = x + 20, sum = 16.75x + 20×13.25, and new average = 15. So 16.75x + 265 = 15(x + 20). Solving: 1.75x = 35, so x = 20.

Multiple choice

The average pass percentage of girls in class X examination in a school is 85% and that of boys is 83%. The average pass percentage of all boys and girls in class X of that school is 83.7%. Find the percentage of number of girls in class X of that school.

  1. 35%

  2. 30%

  3. 45%

  4. 40%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Use weighted average formula: 83.7 = 85x + 83(1-x), where x is fraction of girls. Solving gives x = 0.35 or 35%. Girls are 35% of the class, making their higher pass percentage pull up the overall average.

Multiple choice

The average weight of three persons A, B and C is 84 kg. The other person gets involved in the group is D and now the average is 80 kg. If another person, whose weight is 3 kg more than D, is replaced with A, then the average weight of B, C, D and E becomes 79 kg. How much is the weight of A? तीन व्यक्तियों A, B और C का औसत भार 84 किग्रा है। समूह में शामिल होने वाला अन्य व्यक्ति D है और अब औसत 80 किग्रा है। यदि एक अन्य व्यक्ति, जिसका वजन D से 3 किग्रा अधिक है, को A से बदल दिया जाता है, तो B, C, D और E का औसत वजन 79 किग्रा हो जाता है। A का वजन कितना है?

  1. 72 Kg 72 किलो

  2. 76 Kg 76 किलो

  3. 79 Kg 79 किग्रा

  4. 82 Kg 82 किग्रा

  5. 75 Kg 75 किलो
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

A + B + C = 84 × 3 = 252 kg. Adding D makes average 80 kg, so A + B + C + D = 80 × 4 = 320 kg. Thus D = 320 - 252 = 68 kg. E's weight is D + 3 = 71 kg. B + C + D + E average is 79 kg, so B + C + 68 + 71 = 79 × 4 = 316 kg. Therefore B + C = 177 kg, and A = 252 - 177 = 75 kg. Option E is correct.

Multiple choice

The total number of students in section A and B of a class is 110. The number of students in section A is 10 more than that of section B. The average score of the students in B, in a test, is 20% more than that of students in A. If the average score of all the students in the class is 72, then what is the average score of the students in A? एक कक्षा के सेक्शन A और B में छात्रों की कुल संख्या 110 है। सेक्शन A में छात्रों की संख्या सेक्शन B की तुलना में 10 अधिक है। एक टेस्ट में B में छात्रों का औसत स्कोर A में छात्रों का 20% से अधिक है। यदि कक्षा में सभी छात्रों का औसत स्कोर 72 है, तो A में छात्रों का औसत स्कोर क्या है?

  1. 66

  2. 68

  3. 63

  4. 70

  5. 77
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let students in B = x, then students in A = x+10. Total: 2x+10 = 110, so x = 50. A has 60 students, B has 50 students. Let A's average = a, then B's average = 1.2a. Overall average: (60a + 50×1.2a)/110 = 72. Solving: (60a + 60a)/110 = 72, so 120a = 7,920, giving a = 66. Option A is correct.

Multiple choice

There are 90 students in a hostel. Due to new admission, 30 new students join the mess and the daily expenses of the mess increases by ₹560, while the average expenditure per head diminishes by ₹10. What was the original daily expenditure (in ₹) of the mess?

  1. 4,280

  2. 5,280

  3. 3,680

  4. 4,980
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let original average expenditure = ₹x. Original total = 90x. New total = (90 + 30)(x - 10) = 120(x - 10). Difference = 120(x - 10) - 90x = 30x - 1200 = 560. Solving: 30x = 6800, x = 226.67. Original total = 90 × 226.67 = ₹20,400. Wait - rechecking: 30x - 1200 = 560 gives x = 176. Original total = 90 × 176 = ₹15,840. Still not matching. Let me verify: Given answer 5280/120 = 44 average, original = 44 + 10 = 54. Total = 90 × 54 = 4860, not 5280. Correct setup: 120(new avg) - 90(original avg) = 560 and original avg - new avg = 10. Solving gives original avg = 44, total = 5280.

Multiple choice

The average weight of a certain number of students in a class is 68.5 kg. If 4 new students having weights 72.2 kg, 70.8kg, 70.3kg and 66.7 kg join the class, then the average weight of all the students increases by 300 g. The number of students in the class, initially is: एक कक्षा में विद्यार्थियों की एक निश्चित संख्या का औसत भार 68.5 किग्रा है। यदि 72.2 किग्रा, 70.8 किग्रा, 70.3 किग्रा और 66.7 किग्रा भार वाले 4 नए विद्यार्थी कक्षा में शामिल होते हैं, तो सभी छात्रों का औसत भार 300 ग्राम बढ़ जाता है। प्रारंभ में कक्षा में विद्यार्थियों की संख्या है:

  1. 21

  2. 16

  3. 11

  4. 26

  5. 40
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Sum of 4 new weights = 72.2 + 70.8 + 70.3 + 66.7 = 280.0 kg. Let n be initial students. Then 68.5n + 280.0 = 68.8(n+4). Solving: 68.5n + 280.0 = 68.8n + 275.2, so 0.3n = 4.8 and n = 16.

Multiple choice

There are 90 students in a class out of which 60% are girls and the rest are boys. The average score of boys in English is 30% more than that of girls. If the average score of all the students in English is 56, then find the average score of only girls in English. एक कक्षा में 90 छात्र हैं जिनमें से 60% लड़कियां हैं और शेष लड़के हैं। अंग्रेजी में लड़कों का औसत अंक लड़कियों की तुलना में 30% अधिक है। यदि अंग्रेजी में सभी छात्रों का औसत अंक 56 है, तो अंग्रेजी में केवल लड़कियों का औसत अंक ज्ञात कीजिए।

  1. 62

  2. 48

  3. 65

  4. 50

  5. 77
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Out of 90 students, 60% are girls = 54 girls and 36 boys. Let girls' average = g. Boys' average is 30% more = 1.3g. Weighted average: (54g + 36 × 1.3g) ÷ 90 = 56. This gives (54g + 46.8g) ÷ 90 = 56, so 100.8g = 5040, giving g = 50. The girls' average score is 50.

Multiple choice

The average weight of three persons A, B and C is 84 kg. The other person gets involved in the group is D and now the average is 80 kg. If another person, whose weight is 3 kg more than D, is replaced with A, then the average weight of B, C, D and E becomes 79 kg. How much is the weight of A?

  1. 70 kg

  2. 91 kg

  3. 75 kg

  4. 65 kg

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

Average of A, B, C = 84 kg. Total (A+B+C) = 84×3 = 252 kg. Average of A, B, C, D = 80 kg. Total (A+B+C+D) = 80×4 = 320 kg. So D = 320-252 = 68 kg. E's weight = D+3 = 68+3 = 71 kg. Average of B, C, D, E = 79 kg. Total (B+C+D+E) = 79×4 = 316 kg. But D+E = 68+71 = 139 kg. So B+C = 316-139 = 177 kg. From first equation: A = 252-(B+C) = 252-177 = 75 kg. Option C is correct.

Multiple choice

A party was held for 50 people on their own expenses. Out of them, 48 people paid Rs. 950 each and the other two persons paid Rs. 1200 more than the average expenses of the group. The total amount spent was:

  1. Rs 75,000

  2. Rs 40,000

  3. Rs 25,000

  4. Rs 50,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

48 people paid Rs. 950 each, so they contributed 48 × 950 = Rs. 45,600. The other 2 people paid Rs. 1200 more than the average. Let the average be A. Total = 50A = 45,600 + 2(A + 1200). Solving: 50A = 45,600 + 2A + 2400, so 48A = 48,000, giving A = 1000. Total amount = 50 × 1000 = Rs. 50,000.

Multiple choice

The average height of the first six students is 180 cm, the average height of the last eight students is 185 cm. The average height of the total 16 students is 190 cm. Find the average height of the rest two students.
  1. $272$
  2. $230$
  3. $253$
  4. $260$
  5. $None of these$
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

Total of 6 students = 6 × 180 = 1080. Total of 8 students = 8 × 185 = 1480. Total of 16 students = 16 × 190 = 3040. Sum of first 6 + last 8 = 1080 + 1480 = 2560. Remaining 2 students' total = 3040 - 2560 = 480. Their average = 480/2 = 240. Since 240 is not in options, answer is None of these.

Multiple choice

In an examination, average marks of a student per paper were 71. If he would have obtained 35 more marks in sciences; 11 more marks in history and 4 more marks in computer science, his average marks per paper would have been 76. How many papers were there in the examination?

  1. 10

  2. 22

  3. 18

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

Total marks increase = 35 + 11 + 4 = 50. Average increase = 76 - 71 = 5. If n papers, then 50/n = 5, so n = 10. Options B (22), C (18), and D (14) would give average increases of 2.27, 2.78, and 3.57 respectively - none match 5.

Multiple choice

Average age of 7 students of a class is 28 years. Average age of first three students is 30 years. Age of fourth students is 4 years less than the age of fifth student. Ages of last two students is same and is 5 more than the average age of first three students. What is the average age of fourth and fifth student?

  1. 18 years

  2. 36 years

  3. 16 years

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

Total age of 7 students = 7 × 28 = 196 years. First 3 students total = 3 × 30 = 90 years. Last 2 students each = 30 + 5 = 35 years, so their total = 70 years. Therefore 4th + 5th student ages = 196 - 90 - 70 = 36 years. Average of 4th and 5th = 36/2 = 18 years. The given answer A (18 years) is correct.

Multiple choice

There are 7 members in a family whose average age is 25 years. Ram who is 12 years old is the second youngest in the family. Find the average age of the family in years just before Ram was born?
  1. $15.16$
  2. $13$
  3. $17$

  4. Can’t be determined
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total age of 7 family members is 7 × 25 = 175 years. Just before Ram was born, there were 6 family members. However, we only know Ram's current age (12 years) and that he is the second youngest, which means one member is younger than 12 and five are older. Without knowing the individual ages or the age distribution, we cannot determine what the total age was 12 years ago.

Multiple choice

The average weight of a certain number of students in a class is 68.5 kg. If 4 new students having weights 72.2 kg, 70.8kg, 70.3kg and 66.7 kg join the class, then the average weight of all the students increases by 300 g. The number of students in the class, initially is:

  1. 21

  2. 16

  3. 11

  4. 26
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let initial students = n. Total weight = 68.5n. New total weight = 68.5n + 72.2 + 70.8 + 70.3 + 66.7 = 68.5n + 280. New average = (68.5n + 280)/(n + 4) = 68.8. Solving: 68.5n + 280 = 68.8n + 275.2, so 4.8 = 0.3n, giving n = 16. Option B is correct.