Question

The average age of students in a class is 16 years. When 4 students, with an average age of 13
years and 6 months, joined the class the average age became 15 years and 7 months. How
many students are there after the 4 students joined?​

Answer 1

The number of students is 20.

Given: The average age of students in a class is 16 years. When 4 students, with an average age of 13 years and 6 months, joined the class the average age became 15 years and 7 months.

To find: We have to find the initial number of students.

Solution:

Let the students be x.

The average age of students in a class is 16 years.

So, the total age of x students is 16x.

The average age of 4 students, is 13

years and 6 months.

So, total age will be-

$(13 + \frac{1}{2}) \times 4 \\ \frac{27}{2} \times 4 = 54$

Now the average age became 15 years and 7 months.

So, we can write-

$\frac{(16x + 54)}{x + 4} = 15 + \frac{7}{12} \\ \frac{(16x + 54)}{x + 4} = \frac{187}{12} \\ 192x + 648 = 187x + 748 \\ 5x = 100 \\ x = 20$

So, the number of students is 20.

Answer 2

24 Students after 4 students joined if The average age of students in a class is 16 years and on joining 4 students, with an average age of 13

years and 6 months  the average age became 15 years and 7 months

Given:

• Average age 16 year
• 4 students with average age of 13 years and 6 months joined
• New average age became 15 years and 7 months

To Find:

• Number of students after 4 students joined

Solution:

$\text{Mean}=\dfrac{\text{sum of all the obervations}}{\text{number of the observations}}$

Step 1:

Number of students initially = n

Average age = 16 years

Total Age = 16n years

1 year = 12 Months

Total age = 16n * 12 =  192n years

Step 2:

Joined 4 students

Average age = 13 years and 6 months

Average Age = 13 * 12 + 6  = 162 months

Total Age of 4 students =  162 x 4  = 648 months

Step 3:

Total Age = 192n + 648 month

Total Students = n + 4

New Average age  =  (192n + 648)/(n + 4)

New average age = 15 years  7 months

New average age = 15 * 12 + 7  = 187 months

Step 4:

Equate new average

 (192n + 648)/(n + 4) = 187

=> 192n + 648 = 187n  + 748

=> 5n = 100

=> n = 20

Step 5:

Find  students after joining 4

20 + 4 = 24

24 students after 4 students joined.

Learn More:

Arithmetic mean of nine observation is calculated as 38 . But in ...

brainly.in/question/8318092

43 the average income of a group of 50 persons working in a factory ...

brainly.in/question/11635184