# AVERAGES

Averages can be defined as the central value in a set of data. Average can be calculated simply by dividing the sum of all values in a set by the total number of values. In other words, an average value represents the middle value of a data set. Questions on Averages are regularly asked in different competitive exams.

Formulae: Model Questions

1. The average of 7 consecutive odd numbers if the smallest of those numbers is denoted by k is:

A) k + 4               B) k + 7               C) k + 6             D) 7k

2. The average weight of a class of 20 students is 45 kgs. When a new student whose weight is 40 kgs replaces an old student, the average weight of the whole class decreases by 1 kg. The weight of the replaced student is:

A) 55 kgs            B) 50 kgs           C) 60 kgs           D) 62 kgs

3. There are twice the number of two wheelers as there are three wheelers and the number of four wheelers are equal to the number of two wheelers. The average number of wheels per vehicle is:

A) 2             B) 3             C) 4            D) 5

4. The average age of 10 men increases by 3 years when one of them, whose age is 54 years, is replaced by a woman. What is the age of the woman?

A) 68 years                         B) 82 years                  C) 72 years            D) 84 years

5. The average age of 30 students is 9 years. If the age of their teacher is included, it becomes 10 years. The age of teacher (in years) is..

A) 27              B) 31                 C) 35            D) 40

6. The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

A) 85             B)100              C) 60             D) 50

7. The average for first 50 natural numbers is

A) 22.25         B) 24.25           C) 25       D) 25.5

8. The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 3 : 5 : 7, then the price of cheapest item is...

A) Rs. 9000           B) Rs. 5000

C) Rs. 8000            D) Rs. 10000

9. The average weight of all the 11 players of the Indian Cricket Team is 50 kg. If the average of first six lightest players is 49 kg and that of the six heaviest players is 52 kg, then the average weight of the player who lies in the sixth position when all the 11 players are arranged in the order of increasing or decreasing weight is:

A) 51 kg              B) 52 kg              C) 56 kg            D) none of these

10. The average of all odd numbers up to 100 is

A) 51          B) 50             C) 49.5            D) 49

11. The average of 10 numbers is calculated as 15. It is discovered later on that while calculating the average one number, namely 36, was wrongly read as 26. The correct average is :

A) 20            B) 18             C) 16               D) 14

12. The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The correct (new) mean is :

A) 35.2             B) 36.1              C) 36.5             D) 39.1

13. The average age of eleven cricket players is 20 years. If the age of the coach is also included, the average age increased by 10%. The age of the coach is :

A) 48 years             B) 44 years

C) 40 years             D) 36 years

14. The average of 5 consecutive odd positive integers is 9. The least one among them is..

A) 5           B) 3            C) 1            D) 7

15. Rahul bought 5 socks at Rs.25 each, 10 shirts at Rs.50 each and 15 belts at Rs.35 each. Find the average price of all the articles.

A) Rs.38.33              B) Rs.45             C) Rs.60                D) Rs.50

Key: 1 - C,    2 - C,    3 - B,    4 - D,    5 - D,    6 - A,    7 - D,    8 - A,    9 - C,    10 - B,    11 - C,    12 - C,    13 - B,    14 - A,    15 - A

Explanations

1. From the given data, the first odd number is k. k, k + 2, k + 4, k + 6, k + 8, k + 10, k + 12 If numbers are having common differences, the middle number will be average. So, k + 6 should be the answer.

2. Decreased weight = 20(1) = 20 kg So, The weight of the replaced student is
= New student weight + 20 = 40 kgs + 20
= 60 kgs. 4. Total weight increased = 10(3) = 30 years
Weight of the woman = 54 + 30 = 84 years

5. Age Increased = 31(1) = 31 years
Age of teacher = Initial Average + Age
Increased = 31 + 9 = 40 years.

6. Weight INcreased = 8(2.5 kgs) = 20 kgs

New person Weight = 65kgs + 20 kgs = 85kgs 8. Average price = Rs.15000
So, total price of three items = Rs.45000
3x + 5x + 7x = 45000
15x = 45000, x = 3000
So, the price of cheapest item 3x = Rs. 9000    13. 10%(20 years ) = 2 years increased
Total Age increased = 12(2) = 24 years
So, Age of coach = 24 + 20 = 44 years

14. For Consecutive numbers, the middle number is average.
So, 3rd number = 9
Then 1st number = 9 − 4 = 5 Previous Year Questions [SSC CGL Exam - 2020]

Directions Qs. (1 - 8): Choose the missing term out of given alternatives.

1. What is the average of numbers from 1 to 50 which are multiples of 2 or 5 (correct to one decimal place)

A) 25.4 B) 25.9 C) 26 D) 25.8

Sol: Number of integers divisible by 2 in the range is 25

Number of integers which are divisible by 5 excluding 2 multiples is 5. Ans: D

2. What is the ratio of the average of first eight prime numbers to the average of first ten even natural numbers?

A) 1 : 7           B) 7 : 80              C) 8 : 70          D) 7 : 8

Sol: Average of n even numbers
= n + 1 = 10 + 1 = 11
Average of first 8 prime numbers = So, the ratio = 77 : 88 = 7 : 8

Ans: D

3. What is the product of the average of first ten positive odd numbers and the average of first fifteen positive even numbers?

A) 85.25           B) 44         C) 160           D) 150

Sol: Average of first 10 odd numbers = 10
Average of first 15 even numbers = 15 + 1 = 16
So, product = 10 × 16 = 160

Ans: C

4. In a class of 90 students 60% are girls and the remaining are boys, Average marks of boys are 63 and that of girls are 70. What are the average marks of the whole class?

A) 58.9            B) 65.3            C) 66.7           D) 67.2

Sol: Percentage of boys = 100% − 60% (girls) = 40%
So, Girls : Boys = 3 : 2

Ans: D

5. In a class the ratio of rural to urban students is 4 : 7. In an examination the average percentage marks of the rural and the urban students are respectively 65 and 63. What is the overall average percentage marks of the class (correct to two decimal places)?

A) 65.87%      B) 73.63%      C) 63.73%           D) 64.37%

Sol: Given ratio Rural : Urban = 4 : 7
4 × 65 + 7 × 63
Average = ¾¾¾¾¾¾¾ = 63.73%
11
Ans: C

6. The average score of 40 students in a class test is 45. Later on, it was found that at two places 25 was read as 35 and at one place 38 was read as 32. What is the actual average score of the class?

A) 45.35       B) 39.69           C) 44.65          D) 43.80

Sol:

− (2 × 10 ) + 6
Correct Average = 45 + ¾¾¾¾¾¾¾ = 44.65
40

Ans: C

7. The monthly salary of 60 employees of a factory is Rs.29900. If two officers are getting Rs.90,000 each and the average salary of 8 supervisors is Rs.65,000, then what is the average salary (in Rs.) of the remaining employees?

A) 21080           B) 22680            C) 29080         D) 21880

Sol: Total Salary of 60 employees = 60 × 29900
Let average salary of the remaining employees = x
So, 60 × 29900 = 2 × 90000 + 8 × 65000 + 50(x) Ans: D

8. The average height of some students in a group is 156 cm. If 5 students of average height 160 cm join the group, then the average height of all the students in the group increases by 0.8 cm. What is the initial number of students in the group?

A) 20      B) 10    C) 25     D) 15

Sol: Let the initial number of students in the group be n students. Initial Sum + 5 student sum = Final Sum
156n + 5(160) = 156.8n + 784
0.8n = 800 − 784 = n = 20

Ans: A

Posted Date : 21-04-2022

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