Question

The age of students in a group are in A.P. having comman difference of 3 months. The age of the youngest student in a group is 12 years Sum of ages of all the students in a 375 years. find the number of Students in the group group​

Answer 1

Step-by-step explanation:

answer is given above

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Answer 2

Given,

The student's ages are in A.P.

The common difference  = 3 months.

The younger student's age = 12.

The total age = 375yrs.

To Find,

The count of students in the group.

Solution,

Given that,

The ages of students are in A.P.

The difference between their ages = 3months.

3/12 = 1/4yrs

The total of their age = 375yrs.

Younger one's age =12yrs.

In A.P, the sum of the terms

S = n/2 (2a +(n-1)d)

a =12.

S = n/2 (2*12+ (n-1)1/4)

S = 375

n/2(2*12+(n-1)1/4) = 375

n/2(24+(n-1)1/4) = 375

n(24+(n-1)1/4) = 750

n(24*4+(n-1)) = 750 * 4

n(96+(n-1)) = 3000

96n + $n^{2}$ -n = 3000

95n + $n^{2}$ = 3000

$n^{2}$ + 95n -3000 = 0

Let's factorise it.

$n^{2}$ + 120n -25n -3000 = 0

n(n+120) -25(n +120) = 0

So,

n = -120 or 25

Hence, 25is the total number of students in the group.