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

Find the value of x and y. If Red bag, Blue bag and White bag have 120 , x and y balls with respectively, if Blue bag gives 150 balls to Red bag, he is left with three and half as many balls as White bag. If together they had 180 more balls, each of them would have had 300 balls on an average.

  1. 5:1

  2. 1:5

  3. 3:4

  4. 4:5

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

Set up the equations: (x - 150) = 3.5y from the first condition, and (120 + x + y + 180)/3 = 300 from the second condition. Simplifying gives x + y = 600. Substituting x = 3.5y + 150 gives 4.5y = 450, so y = 100 and x = 500. The ratio x:y = 500:100 = 5:1.

Multiple choice

The average weight of 35 students is 24 kg., if the weight of the teacher is included, the average weight rises by 400 gm. Find the weight of the teacher. 35 विद्यार्थियों का औसत वजन 24 किलो है, यदि शिक्षक का वजन शामिल है, तो औसत वजन 400 ग्राम तक बढ़ जाता है। शिक्षक के वजन का पता लगाएं |

  1. 30 kg./किग्रा.

  2. 34 kg./किग्रा.

  3. 38 kg./किग्रा.

  4. 42 kg./किग्रा.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When the teacher joins, average increases by 0.4 kg for 36 people (35 students + 1 teacher). Total weight increase = 36 × 0.4 = 14.4 kg. Teacher's weight = original average + total increase = 24 + 14.4 = 38.4 kg. However, using the standard formula: Teacher = new average × new count - old average × old count = 24.4×36 - 24×35 = 878.4 - 840 = 38.4 kg, which rounds to 38 kg.

Multiple choice

The average age of A, B, and C is 24 years. 3 years ago the average age of B and C is 20 years. Find the age of A, 9 years hence.

  1. 23

  2. 35

  3. 41

  4. 50

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

Average age of A, B, C = 24, so total age = 24 × 3 = 72 years. 3 years ago, B and C's average was 20, so their total age then = 20 × 2 = 40. Therefore, B and C's current total age = 40 + 6 = 46 years (adding 3 years for each). A's current age = 72 - 46 = 26 years. A's age 9 years hence = 26 + 9 = 35 years.

Multiple choice

In a class of 40 students in an examination in Mathmatics 4 students scored 100 marks 6 got zero and the average of the rest was 40.What is the average of the whole class?

  1. 40

  2. 60

  3. 120

  4. 80
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

4 students scored 100 marks (total 400), 6 scored 0 (total 0). Rest 30 students averaged 40 (total 1200). Total marks = 400 + 0 + 1200 = 1600. Average of 40 students = 1600/40 = 40. The 100s and 0s balance each other out relative to the 40 average.

Multiple choice

Find the value of quantities and state the correct relationship.\newline Quantity I: The age of teacher, if the average age of 38 students is 16. When teacher’s age is included the average increases by 1.\newline Quantity II: The age of teacher, if the average age of 21 students is 37. When teacher’s age is included the average increases by 1/2.\newline

  1. Quantity II ≥ Quantity I

  2. Quantity I < Quantity II

  3. Quantity I > Quantity II

  4. Quantity II ≤ Quantity I

  5. Relation cannot be established or Quantity I = Quantity II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Teacher adds (17-16)×39 = 39 years to total, so age = 16 + 39 = 55. Quantity II: Teacher adds (37.5-37)×22 = 11 years to total, so age = 37 + 10.5 = 47.5. Therefore 55 > 47.5, so Quantity I > Quantity II.

Multiple choice

The average age of class-I and class-II is 15 years. Average age of class-I is 12 years and average age of class-II is 19 years. If number of students in class-I is 48. Then find the number of students in class-II. कक्षा-I और कक्षा-II की औसत आयु 15 वर्ष है । कक्षा-I की औसत आयु 12 वर्ष है और कक्षा-II की औसत आयु 19 वर्ष है । यदि कक्षा-I में छात्रों की संख्या 48 है, तो कक्षा-II में छात्र की संख्या ज्ञात कीजिये ।

  1. 72

  2. 60

  3. 48

  4. 36
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let students in class II be x. Total students = 48+x. Total sum of ages = 48×12 + x×19. Average = (48×12 + x×19)/(48+x) = 15. Cross-multiplying: 576 + 19x = 720 + 15x. Therefore 4x = 144, and x = 36.

Multiple choice

The average of marks scored by the students of a class is 68. The average of marks of the girls in the class is 80 and that of boys is 60. What is the percentage of boys in the class?

  1. 40%

  2. 60%

  3. 65%

  4. 70%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let B boys and G girls with average scores 60 and 80. Overall average is (60B + 80G) / (B + G) = 68. Solving: 60B + 80G = 68B + 68G, giving 12G = 8B, so G/B = 2/3. Therefore B/(B+G) = 3/5 = 60%. This uses weighted averages where the overall score is between the two subgroup averages.

Multiple choice

The average mark of 36 students in section A is 86% and that of 24 students in section B is 96%. Find the average marks of all the students in section A and section B together.

  1. 90%

  2. 88%

  3. 92%

  4. 91%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total students = 36 + 24 = 60. Total marks = (36 × 86) + (24 × 96) = 3096 + 2304 = 5400. Weighted average = 5400/60 = 90%. This is correct. Option B (88%) is below the weighted average, Option C (92%) would require different section sizes or marks, and Option D (91%) has no calculation basis.