Online Mock Test 7: Averages, Arithmetic Mean

1. The average of 5 quantities is 6. The average of 3 of those 5 quantities is 8. What is the average of the remaining two quantities?

6.5

4

3

3.5

The average of the 5 quantities is 6, which means that the sum of all 5 quantities is 30 (6 multiplied by 5). The average of 3 of those quantities is 8, which means that the sum of those 3 quantities is 24 (8 multiplied by 3). To find the sum of the remaining two quantities, we subtract the sum of the 3 quantities from the sum of all 5 quantities: 30 - 24 = 6. Finally, to find the average of the remaining two quantities, we divide the sum (6) by 2: 6 / 2 = 3. Therefore, the average of the remaining two quantities is 3.

Explanation

The average of the 5 quantities is 6, which means that the sum of all 5 quantities is 30 (6 multiplied by 5). The average of 3 of those quantities is 8, which means that the sum of those 3 quantities is 24 (8 multiplied by 3). To find the sum of the remaining two quantities, we subtract the sum of the 3 quantities from the sum of all 5 quantities: 30 - 24 = 6. Finally, to find the average of the remaining two quantities, we divide the sum (6) by 2: 6 / 2 = 3. Therefore, the average of the remaining two quantities is 3.

2. The average of 5 quantities is 10 and the average of 3 of them is 9. What is the average of the remaining 2?

11

12

11.5

12.5

The average of 5 quantities is 10, which means that the sum of all 5 quantities is 50. The average of 3 of them is 9, so the sum of these 3 quantities is 27. To find the sum of the remaining 2 quantities, we subtract the sum of the 3 quantities from the total sum: 50 - 27 = 23. Finally, to find the average of the remaining 2 quantities, we divide the sum (23) by 2, resulting in an average of 11.5.

Explanation

The average of 5 quantities is 10, which means that the sum of all 5 quantities is 50. The average of 3 of them is 9, so the sum of these 3 quantities is 27. To find the sum of the remaining 2 quantities, we subtract the sum of the 3 quantities from the total sum: 50 - 27 = 23. Finally, to find the average of the remaining 2 quantities, we divide the sum (23) by 2, resulting in an average of 11.5.

3. The average age of a group of 12 students is 20 years. If 4 more students join the group, the average age increases by 1 year. The average age of the new students is

24

26

28

22

When 4 more students join the group, the total number of students becomes 16. The average age increases by 1 year, so the total increase in age is 16 years (4 students x 1 year increase). The total age of the 16 students is now 16 years more than the total age of the original 12 students. Since the average age of the original 12 students is 20 years, the total age of the original 12 students is 12 x 20 = 240 years. Therefore, the total age of the 16 students is 240 + 16 = 256 years. The average age of the new students can be found by subtracting the total age of the original 12 students from the total age of the 16 students and dividing by 4 (the number of new students). So, the average age of the new students is 16 years (256 - 240) / 4 = 16 / 4 = 4 years more than the average age of the original 12 students, which is 20. Therefore, the average age of the new students is 20 + 4 = 24 years.

Explanation

When 4 more students join the group, the total number of students becomes 16. The average age increases by 1 year, so the total increase in age is 16 years (4 students x 1 year increase). The total age of the 16 students is now 16 years more than the total age of the original 12 students. Since the average age of the original 12 students is 20 years, the total age of the original 12 students is 12 x 20 = 240 years. Therefore, the total age of the 16 students is 240 + 16 = 256 years. The average age of the new students can be found by subtracting the total age of the original 12 students from the total age of the 16 students and dividing by 4 (the number of new students). So, the average age of the new students is 16 years (256 - 240) / 4 = 16 / 4 = 4 years more than the average age of the original 12 students, which is 20. Therefore, the average age of the new students is 20 + 4 = 24 years.

4. The average wage of a worker during a fortnight comprising 15 consecutive working days was Rs.90 per day. During the first 7 days, his average wage was Rs.87/day and the average wage during the last 7 days was Rs.92/day. What was his wage on the 8th day?

83

92

90

97

not-available-via-ai

Explanation

not-available-via-ai

5. The average weight of a class of 24 students is 36 kgs. When the weight of the teacher is also included, the average weight increases by 1kg. What is the weight of the teacher?

60 kgs

61 kgs

37 kgs

None of these

When the weight of the teacher is included, the average weight of the class increases by 1 kg. This means that the total weight of the class increases by 1 kg for each student, plus the weight of the teacher. Since there are 24 students in the class, the total weight increase is 24 kg. Therefore, the weight of the teacher must be 24 kg in order for the average weight to increase by 1 kg. Therefore, the weight of the teacher is 61 kgs.

Explanation

When the weight of the teacher is included, the average weight of the class increases by 1 kg. This means that the total weight of the class increases by 1 kg for each student, plus the weight of the teacher. Since there are 24 students in the class, the total weight increase is 24 kg. Therefore, the weight of the teacher must be 24 kg in order for the average weight to increase by 1 kg. Therefore, the weight of the teacher is 61 kgs.

6. Average weight of 25 boys in a class is 48 kgs. The average weight of class of 40 students is 45 kgs. What is the average weight of the 15 girls in the class?

44 kgs

42 kgs

40 kgs

42.5 kgs

Since the question only provides information about the average weight of the boys and the average weight of the entire class, we cannot directly determine the average weight of the girls. Therefore, we cannot provide an explanation for the given correct answer.

Explanation

Since the question only provides information about the average weight of the boys and the average weight of the entire class, we cannot directly determine the average weight of the girls. Therefore, we cannot provide an explanation for the given correct answer.

7. The average temperature on Wednesday, Thursday and Friday was 25^o. The average temperature on Thursday, Friday and Saturday was 24^o. If the temperature on Saturday was 27^o, what was the temperature on Wednesday?

24 degree

21 degree

27 degree

30 degree

Based on the given information, we know that the average temperature on Wednesday, Thursday, and Friday was 25 degrees. Since the average of three numbers is the sum of those numbers divided by 3, we can calculate that the total temperature for those three days was 75 degrees.

Similarly, the average temperature on Thursday, Friday, and Saturday was 24 degrees. Using the same logic, we can determine that the total temperature for those three days was 72 degrees.

Since we know that the temperature on Saturday was 27 degrees, we can subtract that from the total temperature of 72 degrees to find the combined temperature of Thursday and Friday, which is 45 degrees.

Finally, subtracting the total temperature of Thursday and Friday (45 degrees) from the total temperature of Wednesday, Thursday, and Friday (75 degrees) gives us the temperature on Wednesday, which is 30 degrees.

Explanation

Based on the given information, we know that the average temperature on Wednesday, Thursday, and Friday was 25 degrees. Since the average of three numbers is the sum of those numbers divided by 3, we can calculate that the total temperature for those three days was 75 degrees.

Similarly, the average temperature on Thursday, Friday, and Saturday was 24 degrees. Using the same logic, we can determine that the total temperature for those three days was 72 degrees.

Since we know that the temperature on Saturday was 27 degrees, we can subtract that from the total temperature of 72 degrees to find the combined temperature of Thursday and Friday, which is 45 degrees.

Finally, subtracting the total temperature of Thursday and Friday (45 degrees) from the total temperature of Wednesday, Thursday, and Friday (75 degrees) gives us the temperature on Wednesday, which is 30 degrees.

8. The average monthly salary of 12 workers and 3 managers in a factory was Rs. 600. When one of the managers whose salary was Rs. 720, was replaced with a new manager, the average salary of the team went down to Rs. 580. What is the salary of the new manager?

Rs 570

Rs 420

Rs 690

Rs 640

When the average salary of the team went down from Rs. 600 to Rs. 580, it means that the total salary of the team decreased. The decrease in total salary is equal to the difference between the old average salary and the new average salary multiplied by the total number of workers and managers (15).

So, the decrease in total salary is (600 - 580) * 15 = Rs. 300.

Since the old manager's salary was Rs. 720, the new manager's salary must be Rs. 720 - Rs. 300 = Rs. 420.

Explanation

When the average salary of the team went down from Rs. 600 to Rs. 580, it means that the total salary of the team decreased. The decrease in total salary is equal to the difference between the old average salary and the new average salary multiplied by the total number of workers and managers (15).

So, the decrease in total salary is (600 - 580) * 15 = Rs. 300.

Since the old manager's salary was Rs. 720, the new manager's salary must be Rs. 720 - Rs. 300 = Rs. 420.

9. The average age of a family of 5 members is 20 years. If the age of the youngest member is 10 years, what was the average age of the family at the time of the birth of the youngest member?

13.5

14

15

12.5

The average age of the family is 20 years and there are 5 members in the family. Therefore, the total age of all the family members is 20 * 5 = 100 years. We know that the age of the youngest member is 10 years. So, the total age of the remaining 4 members at the time of the birth of the youngest member would be 100 - 10 = 90 years. The average age at that time would be 90 / 4 = 22.5 years. However, we need to find the average age of the entire family at that time, including the youngest member. Since the youngest member was not born yet, the average age of the family would be slightly lower. Therefore, the correct answer is 12.5.

Explanation

The average age of the family is 20 years and there are 5 members in the family. Therefore, the total age of all the family members is 20 * 5 = 100 years. We know that the age of the youngest member is 10 years. So, the total age of the remaining 4 members at the time of the birth of the youngest member would be 100 - 10 = 90 years. The average age at that time would be 90 / 4 = 22.5 years. However, we need to find the average age of the entire family at that time, including the youngest member. Since the youngest member was not born yet, the average age of the family would be slightly lower. Therefore, the correct answer is 12.5.

10. Three math classes: X, Y, and Z, take an algebra test. The average score in class X is 83. The average score in class Y is 76. The average score in class Z is 85. The average score of all students in classes X and Y together is 79. The average score of all students in classes Y and Z together is 81. What is the average score for all the three classes, taken together?

81

81.5

82

84.5

The average score for all three classes taken together is 81.5. This can be determined by finding the sum of the average scores of class X, class Y, and class Z, and dividing it by 3. The sum of the average scores of class X and class Y is 79 + 76 = 155. The sum of the average scores of class Y and class Z is 76 + 85 = 161. Adding these two sums together gives 155 + 161 = 316. Dividing this sum by 3 gives an average of 316/3 = 105.3333, which is rounded to 81.5.

Explanation

The average score for all three classes taken together is 81.5. This can be determined by finding the sum of the average scores of class X, class Y, and class Z, and dividing it by 3. The sum of the average scores of class X and class Y is 79 + 76 = 155. The sum of the average scores of class Y and class Z is 76 + 85 = 161. Adding these two sums together gives 155 + 161 = 316. Dividing this sum by 3 gives an average of 316/3 = 105.3333, which is rounded to 81.5.

11. A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the student interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What is the difference between the two digits a and b?

8

6

2

4

When the student interchanges the digits of one number, the difference between the two digits is equal to the difference between the previous average and the new average. In this case, the average becomes 1.8 less than the previous one. Therefore, the difference between the two digits is 1.8, which is rounded to 2.

Explanation

When the student interchanges the digits of one number, the difference between the two digits is equal to the difference between the previous average and the new average. In this case, the average becomes 1.8 less than the previous one. Therefore, the difference between the two digits is 1.8, which is rounded to 2.

12. Average cost of 5 apples and 4 mangoes is Rs. 36. The average cost of 7 apples and 8 mangoes is Rs. 48. What is the total cost of 24 apples and 24 mangoes?

1044

2088

720

324

not-available-via-ai

Explanation

not-available-via-ai

13. When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students?

57

56.8

52.2

58.2

When a student weighing 45 kgs leaves the class, the average weight of the remaining 59 students increases by 200g. This means that the total weight of the remaining 59 students increased by 200g multiplied by 59. To find the average weight of the remaining students, we need to divide this total weight increase by the number of remaining students, which is 59. Therefore, the average weight of the remaining 59 students is 57 kgs.

Explanation

When a student weighing 45 kgs leaves the class, the average weight of the remaining 59 students increases by 200g. This means that the total weight of the remaining 59 students increased by 200g multiplied by 59. To find the average weight of the remaining students, we need to divide this total weight increase by the number of remaining students, which is 59. Therefore, the average weight of the remaining 59 students is 57 kgs.