# Average MCQs for Competitive Examination

## Solve the following problems.

**Q. 41**

The average marks of 50 students in a class was found to be 64. If the marks of two students were incorrectly entered as 38 and 42 instead of 83 and 24 respectively then what is the correct average?

(A) 64.54

(B) 62.32

(C) 61.24

(D) 61.86

**Answer**: (A) 64.54**Explanation**: Average = (50 * 64 + 83 + 24 – 38 -42)/50 = 64.54

**Q. 42**

The average of 12 numbers is 55.5. The average of the first four numbers is 53.4 and that of the next four number is 54.6. The 10th number is greater than the 9th number by 3 but lesser than the 11th and 12th numbers by 2 and 3 respectively. What is the average of the 10th and 12th numbers?

(A) 59.5

(B) 58

(C) 57.5

(D) 56

**Answer**: (A) 59.5**Explanation**: Sum of total number = (12 * 55.5) = 666

The sum of the first four numbers = (4 * 53.4) = 213.6

The sum of the 5th to 8th numbers = (4 * 54.6) = 218.4

Let the 10th number = x; hence 9th number = x – 3, 11th number = x + 2, 12th number = x + 3

Therefore 213.6 + 218.4 + x – 3 + x + x + 2 + x + 3 =666

hence x = 58

Avg of 10th and 12th = (58 + 61)/2 = 119/2 = 59.5

**Q. 43**

Four different positive numbers are written in ascending order. One-third of the average of all the four numbers is 19 less than the greatest of the four numbers. If the average of the first three numbers is 12. The greatest number among the given number is?

(A) 25

(B) 22

(C) 24

(D) 21

**Answer**: (C) 24**Explanation**: Let the numbers are P < Q < R < S

(1/3) * (P + Q + R + S)/4 = S – 19

Hence P + Q + R + S =12S – 228

Again (P + Q + R)/3 = 12

Simplifying both we have S = 24

**Q. 44**

Three numbers are such that if the average of any two of then is added to the third number the sums obtained are 168, 174 and 180 respectively. What is the average of the original three numbers?

(A) 86

(B) 87

(C) 89

(D) 84

**Answer**: (B) 87**Explanation**: Let the numbers be x, y, z

Hence (x + y)/2 +z = 168; (y + z)/2 + x = 174; (z + x)/2 + y = 180…Adding three equations we have (x + y + z) = 261

Hence (x + y +z)/3 = 87

**Q. 45**

The total number of students in class A and B is 96. The number of students in A is 40% more than that of B. The average weight (kg) of the student in B is 50% more than that of the students in A. If the average weight of all the students in A and B taken together is 58 kg then what is the average weight of the student in class B?

(A) 72 kg

(B) 60 kg

(C) 48 kg

(D) 66 kg

**Answer**: (A) 72 kg**Explanation**: A + B = 96; A = 1.4B

Solving A = 56, B = 40

Let Avg weight of students in class A = X

Avg weight of students in class B = (150/100) X = (3/2)X

Hence, 56X + 40*(3/2)X = 58 * 96

116X = 58 * 96

X = 48, Avg weight of the student in class B = (3/2) * 48 = 72

**Q. 46**

In a class of 80 students, 60% participated in games and the rest do not. The average weight of the former group is 5% more than that of the latter and if the average weight of all the students is 51.5 kg, then what is the average weight (in kg) of the former group?

(A) 57.6

(B) 54.6

(C) 60

(D) 52.5

**Answer**: (D) 52.5**Explanation**: Follow the same pattern as Q. 45

**Q. 47**

There are three numbers. If the average of any two of them is added to the third number the sums obtained are 177, 163 and 138. What is the average of the largest and the smallest of the given numbers?

(A) 76

(B) 79

(C) 81

(D) 67

**Answer**: (A) 76**Explanation**: Let the three numbers be x, y, z. Following the same ways as Q. 44 we have

x + y + 2z = 354, y + z + 2x = 326, z + x + 2y = 276

Adding all three (x + y + z) = 239

Solving, x = 87, y = 37, z = 115

Avg. = (37 + 115)/2 = 76

**Q. 48**

A person purchased 12 bags of sugar at the rate of Rs 1200 per bag, 8 bags at the rate of 1500 per bag and 10 bags at the rate of 2100 per bag. What will be the average cost of all the bags together?

(A) 1420

(B) 1680

(C) 1580

(D) 1530

**Answer**: (C) 1580**Explanation**: Avg = (12 * 1200 + 8 * 1500 + 10 * 2100)/30 = 1580

**Q. 49**

In a class of 70 students, 40% are girls and remaining are boys. The average marks of the boys are 63 and that of the girls are 70. What is the average marks of the whole class?

(A) 65.4

(B) 65.8

(C) 65.2

(D) 64.8

**Answer**: (B) 65.8**Explanation**: N/A

**Q. 50**

The average of ‘n’ numbers is 36. If each of 75% of the number is increased by 6 and each of the remaining numbers is decreased by 9, then the new average of the number is

(A) 37.125

(B) 37.75

(C) 38.25

(D) 36.25

**Answer**: (C) 38.25**Explanation**: New total = 36n + n((3/4) * 6 -(1/4) * 9)) = 38.25n

New average = 38.25

**Q. 51**

Given four different numbers, the average of the first three numbers is four times the fourth number and the average of all the four number is 52. What is the average of the first three numbers?

(A) 39

(B) 65

(C) 70

(D) 64

**Answer**: (D) 64**Explanation**: N/A

**Q. 52**

The average of three consecutive odd numbers is 52 more than 1/3 rd of the largest of these numbers. What is the smallest of these numbers?

(A) 79

(B) 75

(C) 81

(D) 77

**Answer**: (D) 77**Explanation: **N/A

**Q. 53**

A batsman scores 87 runs in the 21st match of his career. His average runs per match increases by 2. What was his average before the 21st match?

(A) 45

(B) 46

(C) 44

(D) 43

**Answer**: (A) 45**Explanation**: N/A

**Q. 54**

Of the 3 numbers whose average is 22, the first is 3/8th the sum of the other two. What is the first number?

(A) 16

(B) 20

(C) 22

(D) 18

**Answer**: (D) 18**Explanation**: N/A

**Q. 55**

The mean of marks secured by 50 students in division A of class 10 is 61, 25 students of division B is 57 and that of 50 students of division C is 55. What will be the mean of marks of the students of three divisions of class 10?

(A) 57.1

(B) 56.4

(C) 59.2

(D) 57.8

**Answer**: (D) 57.8**Explanation**: N/A

**Q. 56**

The average weight of 100 students is 32 kg. The average weight of the first 49 students is 30 kg and that of the last 50 students is 34 kg. What is the weight (kg) of the 50th student?

(A) 25

(B) 30

(C) 32

(D) 33

**Answer**: (B) 30**Explanation**: N/A

**Q. 57**

Of the three numbers, the first is twice the second, and the second is twice the third. The average of the reciprocal of the numbers is 7/12. The numbers are

(A) 20, 10, 5

(B) 4, 2, 1

(C) 36, 18, 9

(D) 16, 8, 4

**Answer**: (B) 4, 2, 1**Explanation**: N/A

**Q. 58**

Average age of a team having 12 players is 23 years. If the age of the coach is also included, then the average age increases by 2 years. What is the age (in years) of the coach?

(A) 41

(B) 47

(C) 49

(D) 51

**Answer**: (C) 49**Explanation**: N/A

**Q. 59**

The average of 5 consecutive numbers is A. If the next 3 numbers are also taken, then what will be the new average?

(A) A + 1

(B) A + 1.5

(C) A + 2

(D) A + 2.5

**Answer**: (B) A + 1.5**Explanation**: N/A

**Q. 60**

The average runs conceded by a bowler in 5 matches is 45 and 15.75 in other 4 matches. What is the average runs conceded by the bowler in 9 matches?

(A) 15

(B) 32

(C) 35

(D) 53.5

**Answer**: (B) 32**Explanation**: N/A