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 an examination, Akashi's average marks were 57 per paper. If he had obtained 18 more marks in his English paper and 4 more marks in his Mathematics paper, his average per paper would have been 59. How many more papers except English and Mathematics were there in the examination?

  1. 5

  2. 9

  3. 11

  4. 13
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let n be the total number of papers. Total marks = 57n. New total = 57n + 18 + 4 = 57n + 22. New average = 59 = (57n + 22) / n. 59n = 57n + 22 => 2n = 22 => n = 11. Total papers = 11. Excluding English and Math, there are 11 - 2 = 9 papers.

Multiple choice

The table below gives information about the number of students in a class having different average weights (assume no student's weight is accounted more than once in determining the indicated average weights) Number of Students 3 3 5 3 1 1 5 3 Average Weight 58 60 62 64 66 68 70 72 What is the average weight of the students in the class?

  1. 65.92 kg

  2. 64.83 kg

  3. 62.31 kg

  4. 63.13 kg

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

Weighted average = sum(weight * count) / total count. Total count = 3+3+5+3+1+1+5+3 = 24. Sum = (3*58 + 3*60 + 5*62 + 3*64 + 1*66 + 1*68 + 5*70 + 3*72) = 174 + 180 + 310 + 192 + 66 + 68 + 350 + 216 = 1556. Average = 1556 / 24 = 64.833.

Multiple choice

In a class of 20 students, in an examination of mathematics, 2 students scored 100 marks each, 3 got zero each and the average of the rest was 40. What is the average of the whole class?

  1. 32 marks

  2. 40 marks

  3. 48 marks

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

Total students = 20. 2 students scored 100 (sum = 200). 3 students scored 0 (sum = 0). Remaining 15 students have an average of 40 (sum = 15 * 40 = 600). Total sum = 200 + 0 + 600 = 800. Average = 800 / 20 = 40.

Multiple choice

There are three friends in a village. They are Rajat, Raman and Ranjeet. The total average of their weights is 45 kg. If the average of the weights of Rajat and Raman is 40 kg and that of Raman and Ranjeet is 43 kg, then find the weight of Raman.

  1. 30 kg

  2. 31 kg

  3. 32 kg

  4. 34 kg

  5. 35 kg
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

R+Ra+Rn = 45*3 = 135. R+Ra = 40*2 = 80. Ra+Rn = 43*2 = 86. (R+Ra) + (Ra+Rn) = 80 + 86 = 166. (R+Ra+Rn) + Ra = 166. 135 + Ra = 166. Ra = 31.

Multiple choice

The maximum weight that an elevator can carry is 350 kg. Three men A, B and C enter into the elevator on the ground floor and their average weight is 84 kg. Another man D enters the elevator on the first floor. Now, the average weight of all 4 people in the elevator is 80 kg. At the second floor, A gets out of the elevator and E enters. E's weight is 3 kg more than D, and the present average weight of all 4 people in the elevator is 79 kg. What is A's weight?

  1. 75 kg

  2. 70 kg

  3. 71 kg

  4. 68 kg

  5. 80 kg
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Directions: Solve the following question and mark the best possible option. A class consists of 20 boys and 30 girls. In the mid-semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however, the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is

  1. 9.5

  2. 10

  3. 4.5

  4. 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let B_avg and G_avg be the initial averages. Total initial sum = 20*B_avg + 30*G_avg. Given G_avg = B_avg + 5. Final sum = 20*(B_avg + x) + 30*(G_avg - 3). The final class average increased by 2, so final sum = 50*( (20*B_avg + 30*G_avg)/50 + 2 ). Solving for x gives 9.5.

Multiple choice

At IIM Bangalore class of 1995, Sonali, a first year student has taken 10 courses, earning grades A (worth 4 points each), B (worth 3 points each) and C (worth 2 points each). Her grade point average is 3.2, and if the course in which she get C's were deleted, her GPA in the remaining courses would be 3.333. How many A's, B's and C's did she get?

  1. 3, 1 and 6

  2. 1, 3 and 6

  3. 3, 6 and 1

  4. 1, 6 and 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let A, B, C be the number of courses. A+B+C = 10. (4A+3B+2C)/10 = 3.2 -> 4A+3B+2C = 32. If C's are removed, (4A+3B)/(A+B) = 3.333 = 10/3. 12A+9B = 10A+10B -> 2A = B. Substitute B=2A into A+B+C=10 -> 3A+C=10. Substitute into 4A+3(2A)+2C=32 -> 10A+2C=32 -> 5A+C=16. Subtracting: 2A=6 -> A=3. Then B=6, C=1.

Multiple choice

The average age of a group of 10 students is 12 years. If a teacher joins the group, the average age increases by 1 year. If another teacher of the same age also joins the group, what will be the average age of the whole group?

  1. 11 years

  2. 12.93 years

  3. 13 years

  4. 13.83 years

  5. 14 years
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial: 10 students, avg 12, sum 120. Teacher 1 joins: 11 people, avg 13, sum 143. Teacher 1 age = 143 - 120 = 23. Teacher 2 (same age) joins: 12 people, sum 143 + 23 = 166. New average = 166 / 12 = 13.833.