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

A student finds the average of 10 two digit numbers. If the digit of one of the numbers is interchanged, the average increases by 7.2. The difference between the digits of the two digit number is

  1. 8

  2. 6

  3. 4

  4. 10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the original two-digit number be 10a+b (value 10a+b). When digits are interchanged, it becomes 10b+a (value 10b+a). The difference in values is (10b+a) - (10a+b) = 9(b-a) = 9×(difference of digits). This difference causes the average of 10 numbers to increase by 7.2, meaning the sum increased by 10×7.2=72. So 9×(digit difference) = 72, giving digit difference = 8. Therefore the answer is 8.

Multiple choice

9 person went to a hotel. 8 out of them spent Rs. 120 per person on their food and 9th person spent Rs. 80 more of the average expenditure of 9 persons. What is the amount spent by them ?

  1. Rs.1170

  2. Rs.1230

  3. Rs. 1150

  4. Rs. 1250

  5. Rs. 1125
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let average expenditure be x. Total expenditure = 9x. Eight people spent 120 × 8 = 960. Ninth person spent x + 80. Therefore: 9x = 960 + x + 80, which gives 8x = 1040, so x = 130. Total amount = 9 × 130 = 1170. The ninth person's expenditure is defined relative to the average.

Multiple choice

A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs. 600 from all the faculties. If faculties are 60% of the total staff, then find the average donation should college get from the remaining staff so that college could raise the exact amount for the new building ?

  1. Rs. 300

  2. Rs. 450

  3. Rs. 400

  4. Rs. 500

  5. Rs. 600
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total amount needed be T. Faculties (60% of staff) contributed 75% of T at average Rs. 600. Let total staff be S. Then 0.6S × 600 = 0.75T, which gives 360S = 0.75T, or T = 480S. Remaining 40% staff must contribute 25% of T, which is 0.25 × 480S = 120S. Their average = 120S ÷ 0.4S = Rs. 300. Use weighted averages carefully.

Multiple choice

The average weight of 8 articles increases by 2.5 kg when a new article comes in place of one of those weighing 65 kg. The weight of the new article is- 8 वस्तुओं का औसत भार 2.5 किग्रा. बढ़ जाता है जब एक नयी वस्तु उनमें से एक के स्थान पर आ जाती है जिसका भार 65 किग्रा. है। नयी वस्तु का भार है-

  1. 84 kg./किग्रा.

  2. 85 kg./किग्रा.

  3. 76 kg./किग्रा.

  4. 76.5 kg./किग्रा.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

When one 65 kg article is replaced, the average increases by 2.5 kg for 8 articles. Total increase = 8 × 2.5 = 20 kg. This means the new article weighs 20 kg more than the old one: New weight = 65 + 20 = 85 kg. Option A (84 kg) would only give a 1.93 kg increase, not 2.5 kg. Options C and D (76 kg, 76.5 kg) are less than the original weight and would decrease the average.

Multiple choice

The average price of 10 chocolates is Rs. 12 while the average price of 8 of the chocolates is 11.75. If the price of one of the remaining chocolates is 60% more than the second remaining chocolates. Find the price of cheaper chocolates.

  1. 16

  2. 15

  3. 12

  4. 10

  5. 8
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total sum = 10 × 12 = Rs. 120. Sum of 8 chocolates = 8 × 11.75 = Rs. 94. Sum of remaining 2 chocolates = 120 - 94 = Rs. 26. Let cheaper chocolate cost x, expensive = 1.6x (60% more). So x + 1.6x = 2.6x = 26, x = 10. Cheaper chocolate costs Rs. 10.

Multiple choice

The average height of 32 girls of a class was calculated 165 cm. It was later found that the height of one of the girls in the class was wrongly written as 135 cm, whereas her actual height was 103 cm. What was the actual average height of the class?
  1. $164 cm.$
  2. $166 cm.$
  3. $134 cm.$
  4. $136 cm.$
  5. $Cannot be determined$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum was overstated by 135 - 103 = 32 cm. The actual average decreases by 32/32 = 1 cm from the calculated average. Actual average = 165 - 1 = 164 cm. This is a direct application of the average correction formula.

Multiple choice

The average weight of 40 students in a class is 55 kg. 6 of them whose average weight is 52 kg left the class and another set of 6 students whose average weight is 42 kg, joined the class. What is the new average weight (in kg.) of the class? एक कक्षा के 40 विद्यार्थियों का औसत वजन 55 किग्रा है | यदि इनमे से 52 किग्रा औसत वजन के 6 लोग के स्थान पर 42 किग्रा औसत वजन के 6 नए लोग शामिल हो जाते है तो कक्षा का नया औसत वजन (किग्रा. में) क्या है ?

  1. 51.5

  2. 53.5

  3. 52.5

  4. 54
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total weight of 40 students = 40 × 55 = 2200 kg. Weight of 6 leaving students = 6 × 52 = 312 kg. Weight of 6 joining students = 6 × 42 = 252 kg. New total weight = 2200 - 312 + 252 = 2140 kg. New average = 2140/40 = 53.5 kg. The class size remains 40, so we just divide by 40. Options A (51.5), C (52.5), and D (54) are calculation errors.

Multiple choice

In a test, the average marks of 6 students were 60 however, while crosschecking it was found that the marks of one student were misread as 85 instead of 58 then find the correct average marks? एक परीक्षा में 6 छात्रों के औसत अंक 60 है, जबकि पुनः जाँच में यह पाया गया कि एक छात्र के अंक 58 के स्थान पर 85 पढ़ लिये गए तो नया औसत ज्ञात कीजिए।

  1. 56.5

  2. 55.5

  3. 58

  4. 54.6
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original total marks = 6 × 60 = 360. One student's marks were recorded as 85 instead of 58. Error = 85 - 58 = 27 marks. Corrected total = 360 - 27 = 333. Corrected average = 333/6 = 55.5.

Multiple choice

The average mark of a class in a Maths test is 78. Ritu was the topper with 93 marks. If her mark was wrongly entered as 39, the average of the class decreases by 1. Find the number of students in the class? एक कक्षा में गणित टेस्ट के औसत अंक 78 हैं रितु 93 अंक से सर्वोच्च स्थान प्राप्त करती है। यदि उसके अंक गलती से 39 लेने से कक्षा का औसत एक कम हो जाता है। कक्षा में विद्यार्थी की संख्या ज्ञात कीजिए।

  1. 54

  2. 37

  3. 34

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

Let n students. Correct total = 78n, wrong total = 78n - 93 + 39 = 78n - 54. Average drops by 1, so (78n - 54)/n = 77, giving 78n - 54 = 77n, so n = 54. Option A is correct.

Multiple choice

In an exam, the average marks obtained by the students was found to be 60. After omission of computational errors, the average marks of 100 candidates had to be changed from 60 to 30 and the average with respect to all the examinees came down to 45 marks. The total number of candidates who took the exam, was

  1. 200

  2. 210

  3. 240

  4. 180
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total students be n. Total marks = 60n. After correction, 100 students' average drops from 60 to 30, causing a loss of 100 × (60-30) = 3000 marks. New total = 60n - 3000, and new average is 45. So (60n - 3000)/n = 45, giving 15n = 3000 and n = 200. Option C (240) would come from incorrect equation setup.

Multiple choice

The average weight of 40 students is 35 kg. The average weight of first 25 is 30 kg. and last 16 is 42 kg. What is the weight of the 25th student? 40 छात्रों का औसत भार 35 किग्रा. है | प्रथम 25 का औसत भार 30 किग्रा. है और अन्तिम 16 का औसत भार 42 किग्रा. है | 25 वें छात्र का भार क्या है ?

  1. 20

  2. 24

  3. 22

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

Total weight = 40 × 35 = 1400 kg. Sum of first 25 = 25 × 30 = 750 kg. Sum of last 16 = 16 × 42 = 672 kg. The 25th student is counted in both groups, so weight of 25th = 750 + 672 - 1400 = 22 kg. The double-counting of the 25th student lets us find their individual weight.

Multiple choice

In a class of 66 students there are 33 girls. The average weight of these girls is 61 Kg and average weight of the full class is 66 kgs. What is the average weight of the boys of the class? 66 विद्यार्थियो की एक कक्षा में 33 लड़कियाँ हैं। इन लड़कियों का औसत वजन 61 किग्रा. है और पूर्ण क़क्षा का औसत वजन 66 किग्रा. हैं। कक्षा के लड़कों का औसत वजन क्या है?

  1. 72

  2. 73

  3. 69

  4. 71
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total weight of girls = 33 × 61 = 2013 kg. Total weight of class = 66 × 66 = 4356 kg. Boys' total weight = 4356 - 2013 = 2343 kg. With 33 boys, average = 2343 ÷ 33 = 71 kg.