Online Mock Test 7: Averages, Arithmetic Mean

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.