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## Topic : Averages (Basic to Advance Level)

4. 12 years ago, there were 7 members in Arun’s family & then the average age of the family was 28 years. His father died three years ago from present & then the average age of the family was 26 years. Then his father died at the age of

5. The average weight of three men A, B and C is 65 kg. Another man D joins the group and the average now becomes 68 kg. If another man E whose weight is 4 kg less than that of D, replaces A then the average weight of B, C, D and E becomes 67 kg. Find the weight of A?

6. The average age of 40 teachers in a school in 2007 was 35 years. In 2009, 10 teachers retired from the job, whose average age was 50 years. In 2012, 20 teachers joined the school, whose average age was 30 years. What was the total age of all the teachers in 2015 assuming that no teacher joined or left the school apart from the ones mentioned in the question?

7. The average age of ‘x’ students in class 8 is (x – 6) years. If the two teachers whose age is 36 years and 40 years join the class, then the average age of the peoples in class 8 increases by 2 years. In class 9, there are (x + 35) students out of which 25% are girls. In class 9, if the average age of each girl is 14 years and that of each boy is 16 years, then find the average age of each student in class 9.

8. Average run scored by Virat in 36 innings is 48. Difference between highest and lowest scores scored by him is 151 and if these two innings are excluded then his overall average decreases by 3.5. Find highest score scored by him. (a) 183 (b) 181 (c) 189 (d) 187

9. Present age of ‘A’ is 50% less than that of ‘C’ which in turn is 40% more than the present age of ‘B’. If the average of present ages of ‘A’ and ‘C’ is 1.5 years more than the present age of ‘B’, then find the average present age of ‘A’, ‘B’ and ‘C’.

10. The average number of goals scored per match by a football player in matches where he was in the team of starting 11 is 1.5 and the average number of goals scored by the player in matches where he came on as a substitute is 0.5. The player scored 390 goals more in matches where he was in the team of starting 11 than in matches in which he came on as a substitute. If he played 388 matches in total, find the average number of goals scored by the player per match?

11. The average number of students in each class of a school of classes up to 1 to 12 was 84, in the previous year. In the present year, average number of new students who took admission up to class 5 was 18 and average number of students who left school up to class 5 was also 18. If in this year the average number of students who left the school from class 6 to class 12 was 12 and the present total number of students in school is 1116 then, find the total number of new students who took admission this year.

12. Average salary of 36 employees in a company is Rs. 10,375. Salary of an officer in the company is 125% more than the salary of a worker in the company. Find the salary of all the workers together, if the number of officers in the company is 40% more than the number of workers in the company.

13. The average age of a family having five members is 42 years and the age of the oldest member of the family is 76 years. In the same year, a member whose age is 32 years has married a girl whose age is 30 years and after marriage, the average age of the family (including the bride) reduced by 2 years. If ratio of the age of the rest of three members (other than the oldest member, member who got married and his bride) is 5:14:15, respectively then find the difference between the age of the oldest and the age of the youngest member.

14. There are two groups of persons, A and B, and each group has 5 persons. The average age of persons of group A is 22 years while the average age of persons of group B is 19 years. A person Mohan from group A joins group B and then average age of group A becomes 24 years. Then, Rahim, a person from group A joins group B and the average age of group B becomes 20 years. Now, a person Ram of group B joins group A and the average age of group A becomes 22 years then find the ratio of age of Ram to the age of Mohan?

15. The average number of flights of Indigo, AI and Spicejet coming to Delhi airport is 250. The total number of Indigo and Spicejet planes coming to Delhi airport is 600. Find the average number of Indigo and AI planes coming to Delhi airport if the number of Spicejet planes coming to Delhi airport is twice the number of Indigo planes.

16. The average of the income of ‘A’ in 2019 and 2020 is Rs. 40000. He saves 25% of his income in 2019 such that his savings in both the year is same. If his expenditure in 2020 was equal to his average income of 2019 and 2020, then find the expenditure of ‘A’ in 2019.

17. There are 50 students in a class having equal number of girls and boys. 10 new boys and 10 new girls who have each scored the equal number of marks are added to the class. The average marks of the boys in the class increases by 20% while the average marks of girls decrease by 20%. What was the ratio of the average marks scored by the boys and girls before new students joined?

18. The average age (in years) of a group of people is twice the number of people in the group. A person, X, leaves the group and the average age is still twice the number of people in the group. Now another person, Y, leaves the group and the average age is still twice the number of people in the group. If the ratio of the ages of X and Y is 19 : 17, then find the average age of the group, if one more person, Z, of age 16 years, leaves the group.

19. Present ages of A and B are in the ratio 7: 5, respectively. Present ages of C and D are in the ratio 2: 3, respectively. Present average age of A, B and D is 36 years and the present average age of A, C and D is 34 years. Find the difference between the ages of A and D.

20. Total number of students in three sections ‘A’, ‘B’ and ‘C’ of class V is 120. The average marks obtained by all the students in class V is 54.5. Average marks obtained by students of section ‘B’ and ‘C’ is 56(2/3) and average marks obtained by students of section ‘A’ is 48. Find the number of students in section ‘A’.

21. ‘A’, ‘B’, ‘C’ and ‘D’ are four friends such that average age of any of the three taken together is 43 years, 33 years, 38 years and 42 years, respectively. Find the difference between the age of the youngest and the oldest among the four friends.

22. The average cost price of 3 articles ‘A’, ‘B’ and ‘C’ is Rs. 920 and the average cost price of articles ‘A’ and ‘B’ is Rs. 960. Cost price of article ‘C’ is 5% more than that of article ‘A’. If articles ‘A’, ‘B’ and ‘C’ are sold at profit of 15%, loss of 10% and profit of Rs. 22, respectively, then find the average of their selling prices.

23. A batsman scored runs with an average of ‘x + 45’ in ‘x – 20’ matches. In next 5 matches, he scored runs with an average of 60 due to which his overall average decreased by 5, Find the value of ‘x’.

24. Lorem ipsum dolor sit amet, consectetur adipiscing elit. Ut elit tellus, luctus nec ullamcorper mattis, pulvinar dapibus leo.24. The average weight of ‘b’ boys in a group is 63 kg. A boy whose weight is 147 kg joins the group such that the average weight of the group becomes a prime number in between 65 and 91. Find the value of ‘b + 1’.

25. MPs from 5 different parties A, B, C, D and E are present in the parliament. The average number of MPs from parties A and C is 100 and that from parties B and E is 90. The number of MPs from party B is 50 more than that of party C. The total number of MPs from parties A and E is 230. The number of MPs of party D is 20 more than that of party B. Find the total number of MPs from parties A, E and D.

26. A rocket needs a certain number of tests before launching, it is called Launch vehicle system tests. Let some scores are assigned to it after each test. Now, the average score increases by 1 if the first 5 tests are not considered, and decreases by 1 if the last 5 tests are not considered. If the average scores of the rocket for the first 5 and the last 5 tests are 40 and 60, respectively, then the total number of tests, the rocket needs to over is:

27. In a hotel, total expenses are partly fixed and partly varying linearly with the number of customers. The average expense per customer is Rs. 1750, when there are 30 customers and Rs. 1450 when there are 55 customers. What is the average expense (in Rs.) per customer when there are 100 customers?

28. There are 2 classes X and Y in a college. The average weight of the students in class X and class Y combined is 75 kg. The average weight of students in class X is 45 kg more than the average weight of students in class Y. Which of the following cannot be the ratio of the number of students in classes X and Y, if it is known that the average weights of both the classes are integers?

29. Age of Smith is 13/11 of the age of his younger brother Robert and Johnson is 8 years younger to Robert. If the ratio of age of their father and mother is 10 : 9 and father is 46 years older to Johnson. What is the average age of the father and mother if the average age of the five-member family is 35.2 years?

30. In a school, the average weight of all the boys is 68 kg and that of all the girls is 52 kg. For the school annual day, each male teacher is asked to coordinate the activities of exactly 13 boys and each female teacher is asked to coordinate the activities of exactly 12 girls. If the ratio of male to female teachers is 4 : 1, find the average weight of the students of the school (in kg).

# Answer Key

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**1.** A student studied four subjects in his bachelor’s degree. If the ratio of marks in subject A and B is 1:2, in subject B and C is 2:5 and in subject A and D is 1:4. If she has scored an average of 84 marks in a subject. In how many subjects did she score equal to or greater than 60 marks?

(a) 1

(b) 2

(c) 3

(d) 4

**2.** There are 45 students in a hostel. If the number of student increases by 5, the expenses of the mess increases by Rs.30 per day while the average mess expenditure per head(per day) diminishes by Rs.2. Find the original expenditure of the mess.

(a) Rs. 1180

(b) Rs. 1170

(c) Rs. 1190

(d) Rs. 1150

**3.** In an office of 40 people, the average salary of class-A, class-B and class-C officer is Rs. 600, Rs. 750 and Rs. 1000 a day respectively and there ratio of strength is 5:4:1 respectively. Find the monthly average salary of an officer (in Rs.)? Assume the number of days in a month to be 30.

(a) 21000

(b) 20000

(c) 22000

(d) 23000

(a) 101 years

(b) 110 years

(c) 103 years

(d) 105 years

(a) 77 kg

(b) 75 kg

(c) 72 kg

(d) 78 kg

(a) 1820 years

(b) 1920 years

(c) 1810 years

(d) 1800 years

(a) 14.8 years

(b) 15 years

(c) 14.9 years

(d) 15.5 years

(a) 183

(b) 181

(c) 189

(d) 187

(a) 24 years

(b) 25 years

(c) 31 years

(d) 30 years

(a) 0.571

(b) 1.561

(c) 0.533

(d) None of these

(a) 281

(b) 282

(c) 284

(d) 285

(a) Rs 82, 000

(b) Rs 86, 000

(c) Rs 90, 000

(d) Rs 94, 000

(a) 66 years

(b) 51 years

(c) 56 years

(d) 61 years

(a) 23 : 14

(b) 22 : 15

(c) 14 : 23

(d) Cannot be determined

(a) 200

(b) 125

(c) 175

(d) 150

(a) Rs. 24000

(b) Rs. 32000

(c) Rs. 28000

(d) Rs. 30000

(a) 3 : 17

(b) 5 : 19

(c) 2 : 13

(d) 7 : 20

(a) 8 years

(b) 11 years

(c) 16 years

(d) 28 years

(a) 3 years

(b) 6 years

(c) 9 years

(d) 12 years

(a) 40

(b) 30

(c) 50

(d) 20

(a) 28 years

(b) 24 years

(c) 32 years

(d) 30 years

(a) Rs 945

(b) Rs 930

(c) Rs 890

(d) Rs 875

(a) 40

(b) 60

(c) 50

(d) Can’t be determined

(a) 14

(b) 25

(c) 18

(d) 21

(a) 420

(b) 350

(c) 280

(d) 400

(a) 50

(b) 55

(c) 58

(d) 60

(a) 1258

(b) 1288

(c) 1358

(d) 1368

(a) 8 : 1

(b) 1 : 2

(c) 1 : 5

(d) 2 : 1

(a) 50

(b) 55

(c) 57

(d) 60

(a) 60

(b) 62

(c) 65

(d) 68

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