The average age of 35 students in a class was 15 years 4 months. Three students of ages 18 years 1 month, 17 years 6 months and 15 years 9 months leave the class while 8 students having average age as 16 years 5 months are newly admitted. The raised average age of the class is Options: A . &nbsp15 years 3 month B . &nbsp15 years 6 month C . &nbsp15 years 9 month D . &nbspnone of these

Answer: Option D To find the raised average age of the class after the students leave and new students are admitted, we need to calculate the total age of the students both before and after the changes and then find the average. Let's start by finding the total age of the 35 students before the changes: Average age of 35 students = 15 years 4 months Total age of 35 students = 35 * (15 years + 4 months) Since the age is in years and months, we need to convert the months to years to make the calculation easier: 4 months = 4 / 12 years = 1/3 yearsTotal age of 35 students = 35 * (15 + 1/3) years= 35 * (15 + 1/3)= 35 * 15 + 35 * 1/3= 525 + 35 / 3= 525 + 11.67= 536.67 yearsNext, we need to calculate the total age of the three students who left the class: Age of the first student = 18 years 1 month = 18 + 1/12 years Age of the second student = 17 years 6 months = 17 + 6/12 years Age of the third student = 15 years 9 months = 15 + 9/12 years Total age of the three students = 18 + 1/12 + 17 + 6/12 + 15 + 9/12 = 50.75 yearsSo, the total age of the 35 students after the three students leave the class is: Total age before the changes = 536.67 years Total age after the changes = 536.67 - 50.75 = 485.92 yearsNext, we need to calculate the total age of the 8 newly admitted students: Average age of 8 students = 16 years 5 months Total age of 8 students = 8 * (16 + 5/12) years = 8 * 16.42 years= 131.36 yearsFinally, we need to calculate the total age of the class after the new students are admitted: Total age of the class = Total age before changes + Total age of newly admitted students = 485.92 + 131.36= 617.28 yearsAnd the number of students in the class after the changes is: Total number of students = 35 - 3 + 8 = 40 studentsTherefore, the raised average age of the class after the changes is: Raised average age = Total age of the class / Total number of students = 617.28 / 40= 15.432 yearsAs we can see, the raised average age is not one of the options given, so the correct answer is D. None of these.

The average age of 35 students in a class was 15 years 4 months. Three students

Question

The average age of 35 students in a class was 15 years 4 months. Three students of ages 18 years 1 month, 17 years 6 months and 15 years 9 months leave the class while 8 students having average age as 16 years 5 months are newly admitted. The raised average age of the class is

Options:

A . 15 years 3 month

B . 15 years 6 month

C . 15 years 9 month

D . none of these

Answer: Option D
To find the raised average age of the class after the students leave and new students are admitted, we need to calculate the total age of the students both before and after the changes and then find the average.
Let's start by finding the total age of the 35 students before the changes:

Average age of 35 students = 15 years 4 months
Total age of 35 students = 35 * (15 years + 4 months)
Since the age is in years and months, we need to convert the months to years to make the calculation easier:

4 months = 4 / 12 years = 1/3 yearsTotal age of 35 students = 35 * (15 + 1/3) years= 35 * (15 + 1/3)= 35 * 15 + 35 * 1/3= 525 + 35 / 3= 525 + 11.67= 536.67 yearsNext, we need to calculate the total age of the three students who left the class:

Age of the first student = 18 years 1 month = 18 + 1/12 years
Age of the second student = 17 years 6 months = 17 + 6/12 years
Age of the third student = 15 years 9 months = 15 + 9/12 years
Total age of the three students = 18 + 1/12 + 17 + 6/12 + 15 + 9/12

= 50.75 yearsSo, the total age of the 35 students after the three students leave the class is:

Total age before the changes = 536.67 years
Total age after the changes = 536.67 - 50.75

= 485.92 yearsNext, we need to calculate the total age of the 8 newly admitted students:

Average age of 8 students = 16 years 5 months
Total age of 8 students = 8 * (16 + 5/12) years

= 8 * 16.42 years= 131.36 yearsFinally, we need to calculate the total age of the class after the new students are admitted:

Total age of the class = Total age before changes + Total age of newly admitted students

= 485.92 + 131.36= 617.28 yearsAnd the number of students in the class after the changes is:

Total number of students = 35 - 3 + 8

= 40 studentsTherefore, the raised average age of the class after the changes is:

Raised average age = Total age of the class / Total number of students

= 617.28 / 40= 15.432 yearsAs we can see, the raised average age is not one of the options given, so the correct answer is D. None of these.

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Kani 2021-06-19 01:47:20

Average age of 35 students = 15 years 4 months = 46/3
Total age of 35 students = (46/3)Ã—35 = 1610/3
3 students =18 years 1 month + 17 years 6 months +15 years 9 months = 217/12 + 210/12 + 189/12 =154/3
(35-3) students = 1610/3 - 154/3 =1456/3
Average age of new joining 8 students =16 years 5 months =197/12
Total age of 8 students = (197/12)Ã—8 = 394/3
(32+8) students = (1456/3) + (394/3) = 1850/3
Average age of 40 students = (1850/3)Ã·40 =185/12 =15 years 5 months