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 is 12.05 years. The average age of all girls is 12.5 years and average age of all boys is 11.75 years. If total number of boys is 45, what is the total number of girls? एक कक्षा की औसत आयु 12.05 वर्ष है। सभी लड़कियों की औसत आयु 12.5 वर्ष और सभी लड़कों की औसत आयु 11.75 वर्ष है। यदि लड़कों की कुल संख्या 45 है तो कक्षा में लड़कियों की कुल संख्या क्या है?

  1. 20

  2. 25

  3. 30

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

Using weighted average: (45 × 11.75 + g × 12.5) / (45 + g) = 12.05. Solving gives 528.75 + 12.5g = 542.25 + 12.05g, so 0.45g = 13.5, thus g = 30. Options A, B, and D don't satisfy the weighted average equation.

Multiple choice

The average of 20 boys and their teacher is 10 years. When the teacher's age is excluded, the average age decreases by 2 years, the age of teacher is ? 20 लड़कों और उनके अध्यापक की औसत उम्र 10 वर्ष है। जब अध्यापक की उम्र निकाल दी जाती है। तो औसत 2 वर्ष कम हो जाता है। तो अध्यापक की उम्र क्या है?

  1. 40 yr./वर्ष

  2. 50 yr./वर्ष

  3. 60 yr./वर्ष

  4. 70 yr./वर्ष
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total age of 21 people (20 boys + teacher) = 21 × 10 = 210 years. When teacher is excluded, average drops to 8 years (decrease of 2). Total age of 20 boys = 20 × 8 = 160 years. Therefore teacher's age = 210 - 160 = 50 years.

Multiple choice

The average marks obtained by 20 students was calculated to 35. Further it was found that the marks of one student was wrongly read as 45 instead of 85. The correct average is- एक कक्षा में 20 विद्यार्थियों का औसत अंक 35 ज्ञात किया जाता है लेकिन बाद में यह पाया जाता है कि एक बच्चे के अंक 85 के स्थान पर 45 पढ़ लिये जाते हैं, तो सही औसत है-

  1. 37

  2. 33

  3. 33.5

  4. 37.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The difference in marks is 85 - 45 = 40. This difference should be distributed among 20 students, so the correction to the average is 40/20 = 2. The correct average is 35 + 2 = 37.

Multiple choice

The average age of 27 girls and the teacher is 14 years. When the teacher's age is excluded, the average age decreases by 1. What is the age (in year) of teacher? 27 लड़कियों और अध्यापक की औसत आयु 14 वर्ष है। यदि अध्यापक की आयु निकाल दी जाए, तो औसत आयु में 1 की कमी हो जाती है। अध्यापक की आयु (वर्षों में) क्या है?

  1. 41

  2. 42

  3. 39

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

Let the teacher's age be T. Total age of 27 girls + teacher = 28 × 14 = 392 years. When teacher excluded, 27 girls' average = 13 years. Total age of 27 girls = 27 × 13 = 351 years. Teacher's age = 392 - 351 = 41 years. The teacher is older than the average, which makes sense.

Multiple choice

A student bought 4 books for Rs. 120 from one bookshop and 6 books for Rs. 150 from another. The average price (in rupees) of each book? एक छात्र ने एक किताब की दुकान से 120 रू. में 4 किताबें खरीदी। दूसरी दुकान से 150 रू. में 6 किताबें खरीदी तो प्रत्येक किताब का औसत मूल्य क्या था?

  1. ₹ 27

  2. ₹ 27.50

  3. ₹ 135

  4. ₹ 138
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total cost = 120 + 150 = Rs. 270. Total books = 4 + 6 = 10. Average price = Total cost / Total books = 270/10 = Rs. 27. Option C (₹135) is a trap — it's the sum of both purchase amounts, not the average.

Multiple choice

There are 1600 students in a college, whose average weight is 50 kg. If average weight of boys is 54 kg. and average weight of girls is 38 kg. then find the number of girls in the school. एक स्कूल में 1600 छात्र हैं, जिनका औसत भार 50 किग्रा. है | यदि लड़कों का औसत भार 54 किग्रा. है और लड़कियों का औसत भार 38 किग्रा. है, तो लड़कियों की संख्या ज्ञात कीजिये |

  1. 400

  2. 800

  3. 1200

  4. 1000
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using alligation method: Average 50 kg is between boys (54 kg) and girls (38 kg). The ratio of boys to girls is (50 - 38):(54 - 50) = 12:4 = 3:1. If 3 parts = 1200 boys, then 1 part = 400 girls. Alternatively: 54x + 38(1600 - x) = 50 × 1600. Solving gives x = 1200 boys, so girls = 400.

Multiple choice

The average weight of P, Q, R is 40 kg. when S joins them the average becomes 44 kg. If another student T, who is 3 kg. more then S joins them, the average of 4 student Q, R, S and T becomes 43 kg. Find the weight of P?

  1. 70

  2. 67

  3. 65

  4. 63

  5. 61
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Average of P, Q, R is 40, so P+Q+R = 120. When S joins, average becomes 44 for 4 people, so P+Q+R+S = 176. Subtracting gives S = 56 kg. T is 3 kg more than S, so T = 59 kg. Average of Q, R, S, T is 43, so Q+R+56+59 = 172, giving Q+R = 57. From P+Q+R = 120, we get P = 120 - 57 = 63 kg.

Multiple choice

In an examination, Ritesh got 54 percent marks, Shekhar got 68 percent marks and Rinku got 74 percent marks.The maximum marks in the examination is 850.What is the approximate average marks got by all the three boys ?

  1. 555

  2. 545

  3. 565

  4. 575

  5. 585
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Ritesh: 54% of 850 = 459. Shekhar: 68% of 850 = 578. Rinku: 74% of 850 = 629. Average = (459 + 578 + 629)/3 = 1666/3 = 555.33. The approximate average is 555, matching option A.

Multiple choice

The average marks of 45 students in a science exam is 64. Later it is found that three marks 68, 58 and 72 were wrongly written as 86,46 and 58.The average after mistake were rectified is. विज्ञान की परीक्षा में 45 छात्रों के औसत अंक 64 है। बाद में पता चलता है कि तीन अंक 68, 58 और 72 गलती से 86, 46 और 58 लिख लिए गये थे। गलतियां सुधारने के बाद औसत हैः

  1. 66

  2. 62

  3. 64.9

  4. 64.17
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total marks = 45 × 64 = 2880. Wrong total = 86 + 46 + 58 = 190. Correct total = 68 + 58 + 72 = 198. Difference = 198 - 190 = 8. New average = (2880 + 8) / 45 = 2888/45 = 64.17.

Multiple choice

If average weight of 8 articles is 152 gm. If two more articles having weight 144 gm. and 155 gm. are included,then what is new average weight? 8 वस्तुओं का औसत वजन 152 ग्राम है | 144 ग्राम और 155 ग्राम की दो वस्तुएं और शामिल की जाती हैं तो नया औसत वजन क्या है?

  1. 151 ग्राम

  2. 150.5 ग्राम

  3. 151.5 ग्राम

  4. 152.5 ग्राम
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

8 articles average = 152, total weight = 8×152 = 1216 gm. New total = 1216 + 144 + 155 = 1515. New count = 10. New average = 1515/10 = 151.5 gm.

Multiple choice

A train travels 10 km in the first quarter of an hour, 16 km in the second quarter and 40 km in the third quarter. Find the average speed of the train per hour over the entire journey?
  1. $60 km/h$
  2. $88 km/h$
  3. $75 km/h$
  4. $77 km/h$
  5. $79 km/h$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total distance = 10 + 16 + 40 = 66 km. Total time = 3 quarters of an hour = 3/4 hour = 45 minutes. Average speed = Total distance ÷ Total time = 66 ÷ (3/4) = 66 × 4/3 = 22 × 4 = 88 km/h (option B).