# AVERAGES

1. A total number of students in section A and B of a class is 60. The ratio of the number of students in A and B is 3 : 2. The average weight of students in section B is 20% more than that of the students in section A. If the average weight of all the students in class is 54 kg, then what is average weight of the students in section B?

A) 58.2    B) 57.9    C) 60    D) 56.4    E) 79

Explanation: A : B

Average: 5x : 6x

No. of Students:   3 : 2

27x = 270

x = 10

Required Average = 6x ⇒ 6 × 10 = 60

Ans:

2. A car owner buys petrol at Rs.7.5, Rs.8, and Rs.8.5 per litre for three successive years. What approximately the average cost per litre if he spends Rs.4000 each year?

A) 7.98     B) 8    C) 8.5   D) 9    E) 9.5

Explanation

Ans: A

3. Out of 10 teachers of a school one teacher retires and at his place, a new teacher of age 30 years joins. As a result of it, the average age of the teachers is reduced by 2 years. The age of the retired teacher is......

A) 60 years    B) 58 years   C) 56 years   D) 50 years   E) 52 years

Explanation:

0 × (x − 2) − 2 × 10 = 30

30 + 2 × 10 = 50

Ans: D

4. A batsman has scored an average of 46 runs for a certain number of innings played in England. When he came back to India, he played another two test matches of two innings each and scored at an average of 55 runs. For the innings in England and in India taken together, he has improved his average by 2 runs over the matches played in England and the number of innings played in England was?

A) 16     B) 14     C) 18     D) 20     E) 22

Explanation: Average: 46   55   48

↑     ↑      ↑

Innings: x    4 x + 4

46 × x + 55 × 4 = (x + 4) × 48

46x + 220 = 48x + 192

2x = 28

x = 14

Ans: B

5. The average of 13 numbers is 47. The average of the 1st three numbers is 39 and that of next seven numbers is 49. The 11th number is three times the 12th number and 12th number is 9 more than the 13th number. What is the average of 11th and 13th numbers?

A) 59.5    B) 54.5    C) 56     D) 55.5    E) 56.5

Explanation:

Sum of numbers = 13 × 47 = 611

Sum of 1st 3 numbers = 3 × 39 = 117

Sum of 7 numbers = 7 × 49 = 343

Sum of remaining numbers = 611 − (117 + 343) = 151

11th number : 12th number : 13th number

3x : x : x − 9

5x − 9 = 151

5x = 160

x = 32

Average of 11th & 13th numbers

Ans: A

6. The average presence of students of a class in a college on Monday, Tuesday and Wednesday is 32 and, on the Wednesday, Thursday, Friday and Saturday is 30. If the average number of students on all the six days is 26 then the number of students who attended the class on Wednesday is?

A) 50     B) 40     C) 60     D) 70    E) 30

Explanation: Total no. of students on Monday,

Tuesday & Wednesday = 3 × 32 = 96

Total no. of students on Wednesday,

Thursday, Friday, Saturday = 4 × 30 = 120

Total no. of students on all six days = 6 × 26 = 156

Total no. of students on Monday & Tuesday = 156 − 120 = 36

Total no. of students on Wednesday = 96 − 36 = 60

Ans: C

7. The average score of class X is 75. The average score of class Y is 68. The average score of class Z is 81. The average score of X and Y is 70 and average score of Y and Z is 76. What is the average score of X, Y and Z?

A) 76.6   B) 80.50    C) 75.86    D) 78.48     E) 78

Explanation:

Let assume average is 68

= 75.86

Ans:

8. The average of 18 observations was calculated and it was 124. Later it was discovered that two observations 46 and 82 were incorrect. The correct values are 64 and 28. The correct average of 18 observations is?

A) 123    B) 137    C) 121    D) 122    E) 124

Explanation: (82 + 46) − (64 + 28) = 36

= 122

Ans: D

9. In a school with 600 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years 9 months, then the number of girls in the school is.....

A) 150   B) 250    C) 350    D) 450    E) 400

Explanation: Boys     Girls

12          11

4 → 600

1 → 150

Ans: A

10. A class of 20 boys and 30 girls in the mid semester examination, the average score of the girls was 5 higher than that of the boys. In the final exam, however the average score of the girls dropped by 3 while the average score of the entire class increased by 2. The increase in the average score of the boys is......

A) 9.5     B) 10     C) 4.5     D) 6     E) 8

Explanation Boys     Girls        Total

20        30           50

Ans: A

11. There are 720 students in a hostel. If the number of students increased by 40, the expenses of the mess increased by Rs.40 per day while the average expenditure per head reduced by Rs 5, then find the original expenses of the mess?

A) 96     B) 106     C) 86     D) 56     E) 76

40(x − 5) − 5 × 720 = 40

40x − 200 − 3600 = 40

40x = 3840 x = 96

Ans:

12. The bowling average of Meghana was 20. She decreases her bowling average by 5. When she takes all the 10 wickets for 30 runs in his last match, then find the number of wickets taken by her before the last match?

A) 21     B) 24     C) 25     D) 35     E) 28

10 × 15 − 5 × x = 30

150 − 30 = 5x

x = 24

Ans: B

13. The average weight of 7 students in class is 64. It was noticed later that the weight of one student is wrongly taken as 42 instead of 63, then find the new average weight of the class?

A) 65     B) 61     C) 58     D) 67      E) 79

Explanation:

= 64 + 3 = 67

Ans:

14. In a group, the average age of 12 persons is 77. If two new persons were joined such as 36 and 48 in the place of 63 and 84 respectively, then find the new average age of the group?

A) 67.25   B) 70.75    C) 68.25    D) 71.75      E) 72.15

⇒ 71.75

Ans: D

15. The average price of 10 English books is Rs.400 and the average price of a certain number of Hindi books is Rs.550. The average price of both English and Hindi books is Rs.500. What is the difference between the number of Hindi books and English books?

A) 20     B) 40     C) 60     D) 10     E) 30

Explanation: English       Hindi

1 → 10

2 → 20

x = 20

Required difference = 20 − 10 = 10

Ans: D

Posted Date : 14-08-2023

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