Average Aptitude

The concept of average is crucial in statistics and everyday mathematics. It is commonly used to find the central value or a typical value of a set of numbers. The average is calculated by adding all the numbers together and then dividing by the count of the numbers. It is a simple yet powerful tool for summarizing and understanding data.

1. Find the average of the first 50 natural numbers.

Average = (Sum of all numbers) / (Number of items).
Sum of first n natural numbers = n(n+1)/2.
For the first 50 numbers, sum = 50 * 51 / 2 = 1275.
Average = 1275 / 50 = 25.5.

2. The average of 8, 17, 7, 14, 20, and 15 is:

Average = (Sum of all numbers) / (Number of items).
Sum = 8 + 17 + 7 + 14 + 20 + 15 = 81.
Number of items = 6.
Average = 81 / 6 = 13.5.

3. A student's marks were wrongly entered as 83 instead of 63. Due to that, the average marks for the class got increased by 0.5. The number of students in the class is:

Difference in marks = 83 - 63 = 20.
Since the average increased by 0.5, the number of students = Difference / Increase in average = 20 / 0.5 = 40.

4. The average weight of 16 boys in a class is 50.75 kg. If the weight of the teacher is included, the average rises by 1 kg. The weight of the teacher is:

Total weight of 16 boys = 16 * 50.75 kg = 812 kg.
Average weight of 17 people (16 boys + teacher) = 51.75 kg.
Total weight of 17 people = 17 * 51.75 kg = 879.75 kg.
Weight of the teacher = Total weight of 17 people - Total weight of 16 boys = 879.75 kg - 812 kg = 67.75 kg.

5. The average age of 30 kids is 9 years. If the teacher's age is included, the average age becomes 10 years. The age of the teacher is:

Total age of 30 kids = 30 * 9 = 270 years.
Average age of 31 people (30 kids + teacher) = 10 years.
Total age of 31 people = 31 * 10 = 310 years.
Age of the teacher = Total age of 31 people - Total age of 30 kids = 310 years - 270 years = 40 years.

6. The average of 20 numbers is 50. If two numbers, 35 and 40 are discarded, what is the new average?

Total sum of 20 numbers = 20 * 50 = 1000.
Sum of the remaining 18 numbers = 1000 - (35 + 40) = 925.
New average = 925 / 18 = 51.5.

7. Find the average of the first 100 even numbers.

First even number = 2, last even number = 200.
Average = (First number + Last number) / 2 = (2 + 200) / 2 = 101.

8. A cricketer has a certain average for 10 innings. In the eleventh inning, he scores 108 runs, thereby increasing his average by 6 runs. His new average is:

Let the original average be x.
Total runs for 10 innings = 10x.
Total runs for 11 innings = 10x + 108.
New average = (10x + 108) / 11 = x + 6.
So, 10x + 108 = 11x + 66.
x = 42.
New average = x + 6 = 48.

9. The average temperature for Tuesday, Wednesday, and Thursday is 37 degrees. The average for Wednesday, Thursday, and Friday is 38 degrees. If the temperature on Friday is 39 degrees, what was it on Tuesday?

Total temperature for Tuesday, Wednesday, Thursday = 3 * 37 = 111 degrees.
Total temperature for Wednesday, Thursday, Friday = 3 * 38 = 114 degrees.
Temperature on Friday = 39 degrees.
Temperature on Tuesday = Total temperature for Tuesday, Wednesday, Thursday - Total temperature for Wednesday, Thursday = 111 - (114 - 39) = 36 degrees.

10. The average weight of 5 men is increased by 2 kg when one of the men, who weighs 60 kg, is replaced by a new man. What is the weight of the new man?

Total increase in weight = 5 * 2 = 10 kg.
Weight of new man = 60 kg + 10 kg = 70 kg.

11. The average age of a class of 22 students is 21 years. The average increases by 1 when the teacher's age is also included. What is the age of the teacher?

Total age of 22 students = 22 * 21 = 462 years.
Total age of 23 people (22 students + 1 teacher) = 23 * 22 = 506 years.
Age of the teacher = 506 - 462 = 44 years.

12. The average score of a batsman after playing 13 innings was 42. In the 14th inning, he scores 54 runs. What is his new average?

Total runs after 13 innings = 13 * 42 = 546.
Total runs after 14 innings = 546 + 54 = 600.
New average = 600 / 14 = 42.857 ≈ 43.

13. The average of 7 consecutive numbers is 20. What is the largest number?

If the average is 20, the middle number is 20.
The numbers are 17, 18, 19, 20, 21, 22, 23.
The largest number is 23.

14. The average age of a husband, wife, and their child 3 years ago was 27 years. The average age of the husband and the wife 5 years ago was 29 years. What is the present age of the child?

Total age of husband, wife, and child 3 years ago = 3 * 27 = 81 years.
Total age of husband and wife 5 years ago = 2 * 29 = 58 years.
Present age of the child = (81 + 3 * 3) - (58 + 2 * 5) = 8 years.

15. The average marks of 30 students in a class is 58. When 5 new students join, the new average becomes 56. What is the average marks of the new students?

Total marks of 30 students = 30 * 58 = 1740.
Total marks of 35 students = 35 * 56 = 1960.
Total marks of 5 new students = 1960 - 1740 = 220.
Average marks of new students = 220 / 5 = 44.

16. The average of 9 numbers is 50. If the average of the first five is 54 and that of the last three is 52, what is the sixth number?

Total of 9 numbers = 9 * 50 = 450.
Total of first 5 numbers = 5 * 54 = 270.
Total of last 3 numbers = 3 * 52 = 156.
Sixth number = Total - (Sum of first 5 + Sum of last 3) = 450 - (270 + 156) = 24.

17. A student has an average of 80 in 5 subjects. If he scores 90 in the sixth subject, what is his new average?

Total marks in 5 subjects = 5 * 80 = 400.
Total marks in 6 subjects = 400 + 90 = 490.
New average = 490 / 6 = 81.67 ≈ 82.

18. The average of 4 consecutive even numbers is 17. What is the largest number?

Let the numbers be x, x+2, x+4, and x+6.
Average = (x + x+2 + x+4 + x+6) / 4 = 17.
4x + 12 = 68.
x = 14.
Largest number = x + 6 = 20.

19. The average height of 25 boys is 1.4 meters. When 5 new boys join, the average height increases by 0.1 meters. What is the average height of the new boys?

Total height of 25 boys = 25 * 1.4 = 35 meters.
Total height of 30 boys = 30 * 1.5 = 45 meters.
Total height of 5 new boys = 45 - 35 = 10 meters.
Average height of new boys = 10 / 5 = 2 meters.

20. The average weight of a class of 24 students is 50 kg. If the weight of the teacher is added, the average increases by 2 kg. What is the weight of the teacher?

Total weight of 24 students = 24 * 50 = 1200 kg.
Average weight of 25 people (24 students + teacher) = 52 kg.
Total weight of 25 people = 25 * 52 = 1300 kg.
Weight of the teacher = 1300 - 1200 = 100 kg.