Average Question and Answers -1

Quantitative Aptitude (Averages)

Below are the multiple-choice questions extracted from the provided document, complete with detailed mathematical explanations formatted for clarity.

1. If a person with age 45 joins a group of 5 persons with an average age of 39 years. What will be the new average age of the group?

• (a) 40
• (b) 46
• (c) 42
• (d) 49

Correct Answer: (a) 40

Explanation:
Step 1: Total age of original 5 persons = 39 × 5 = 195 Step 2: Total age after adding new person = 195 + 45 = 240 Step 3: New number of persons = 5 + 1 = 6 Step 4: New Average =

240 6

= 40

2. The average marks of 30 students in a section of class X are 20 while that of 20 students of second section is 30. Find the average marks for the entire class X?

• (a) 22
• (b) 36
• (c) 24
• (d) 38

Correct Answer: (c) 24

Explanation:
Step 1: Total marks of first section = 30 × 20 = 600 Step 2: Total marks of second section = 20 × 30 = 600 Step 3: Total students = 30 + 20 = 50 Step 4: Combined Average =

600 + 600 50

= 24

3. The average of 10 consecutive numbers starting from 21 is:

• (a) 25
• (b) 31
• (c) 26
• (d) 25.5

Correct Answer: (d) 25.5

Explanation:
Step 1: The series starts at 21 and has 10 numbers, so the last number is 30. Step 2: For consecutive numbers, Average =

First + Last 2

Step 3: Average =

30 + 21 2

= 25.5

4. The average of 3 numbers is 17 and that of the first two is 16. Find the third number.

• (a) 15
• (b) 16
• (c) 17
• (d) 19

Correct Answer: (d) 19

Explanation:
Step 1: Sum of 3 numbers = 17 × 3 = 51 Step 2: Sum of first 2 numbers = 2 × 16 = 32 Step 3: Third number = 51 - 32 = 19

5. Three math classes x, y and z takes a test. The average score of class x is 83, The average score of class y is 76 and The average score of class z is 85. What is the average score of classes x, y and z?

• (a) 81.5
• (b) 80.5
• (c) 83
• (d) None

Correct Answer: (a) 81.5

Explanation:
Step 1: Using the allegation method (implied in solution), the ratio of students X:Y:Z is derived as 3:4:5. Step 2: Weighted Average =

3(83) + 4(76) + 5(85) 3 + 4 + 5

Step 3: Calculation: 83 +

-7(4) + 2(5) 12

= 81.5

6. Three years ago, the average age of A, B and C was 27 years and that of B and C 5 years ago was 20 years. A's present age is:

• (a) 30 years
• (b) 35 years
• (c) 40 years
• (d) 48 years

Correct Answer: (c) 40 years

Explanation:
Step 1: Present sum of A, B, C = (27 + 3) × 3 = 90 Step 2: Present sum of B, C = (20 + 5) × 2 = 50 Step 3: A's present age = 90 - 50 = 40

7. The average of the first fifty multiples of 7 is:

• (a) 350
• (b) 121.5
• (c) 280
• (d) 178.5

Correct Answer: (d) 178.5

Explanation:
Step 1: Using the formula for AP average: 7 ×

50 + 1 2

Step 2: 7 × 25.5 = 178.5

8. Two students with marks 50 and 54 leave class A and move to class B. As a result the average marks of the class A fall from 48 to 46. How many students were there initially in the class A?

• (a) 6
• (b) 3
• (c) 7
• (d) 4

Correct Answer: (a) 6

Explanation:
Step 1: Marks leaving = 50 + 54 = 104 Step 2: The average drops by 2 marks (48 - 46). Step 3: Based on the deviation, the initial number of students is calculated as 6.

9. The average of a number and its square is 5 times the number. The number is:

• (a) 9
• (b) 17
• (c) 29
• (d) 295

Correct Answer: (a) 9

Explanation:
Step 1:

x + x² 2

= 5x Step 2: x + x² = 10x Step 3: x² = 9x ⇒ x = 9

10. The age of Shaurya and Kauravki is in the ratio 2:6. After 5 years, the ratio of their ages will become 6:8. Find the average of their ages after 10 years.

• (a) 12
• (b) 13
• (c) 17
• (d) 24

Correct Answer: (a) 12

Explanation:
Step 1: The solution indicates calculating the average after 10 years. Step 2: Future ages derived in solution: 14 + 10 = 24 (sum). Step 3: Average =

24 2

= 12