Math, asked by priyankadogra8599, 9 months ago

The average age of 30 students of a class is 14
years 4 months. After admission of 5 new students
in the class the average becomes 13 years 9
months. The youngest one of the five students is 9
years 11 months old. The average of the remain-
ing 4 new students is​

Answers

Answered by DrNykterstein
2

Total number of students in the class = 30

Given that the mean of the ages of these 30 students is 14 years 4 months

Convert the age from years/months to months only.

So,

Mean becomes ( 14×12 + 4 )

{ Since, 1 year = 12 months }

==> 168 + 4

==> 172

But we know that,

Mean = Sum of all observations / Number of observations

☛ putting the values in the formula

☛ 172 = sum of ages of the students / 30

∴ sum of ages of the students = 5160

Also,

5 new students are added to the class, Now

Given,

Total number of students = 30 + 5 ==> 35

Mean = ( 13×12 + 9 ) ==> 165

Again,

Mean = Sum of the ages of all students / total number of students

☛ 165 = sum of the ages of all students / 35

∴ sum of the ages of all students = 5775

Now,

Sum of the ages of the five new students = ( sum of the ages after adding the five new students ) - ( sum of the ages before adding the five students )

☛ sum of the ages of five new students = 5775 - 5160

∴ sum of the ages of five new students = 615 ...(1)

Also,

The youngest of the five students is 9 years 11 months old or ( 9 × 12 + 11) ==> 119 months old

In eq.(1) ,

☛ sum of the ages of the five new students = 615

By subtracting the age of the youngest student from the five new students, we will get the sum of the ages of the remaining four students:

☛ sum of the ages of 4 students = 615 - 119

∴ sum of the ages of 4 students = 496

We now have,

Sum of the ages of the four students = 496

Number of students = ofcourse , 4 students

So,

Mean = Sum of the ages of the four students / Number of students

☛ Mean = 496 / 4

☛ Mean = 124

We got , Mean = 124 months , ( Convert it into years/months )

==> 12 × 10 = 120

==> 124 months = 10 years 4 months

Hence, Mean of the remaining four students is 10 years 4 months

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