Question

ages of boys are group in ap with common different of 3 month. age of youngest boy in the group is 12 years.some of ages of all the boys in the group is 375 years.find the number of boys in group.​

Answer 1

Step-by-step explanation:

Here, the total sum of ages i. e. Sn=375years

= 375 x12 = 4500months (1 year =12months )

First term (a) = 12 years. i. e 144months

Common difference(d)= 3months

Total number of boys (n)=?

ACCORDING TO FORMULA

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

=4500=n/2(2x144 +(n-1)3)

=4500x2=n(288+3n-3)

=9000=n(285+3n)

=9000=285n+3n^2

=3n^2+285n-9000=0

Divide throughout by 3

=n^2 +95n-3000

Solve this quadratic equation through factorisation method

The factors are -120and 25

(Note:- This quadratic equation can also be solved through completing square method or formula method)

=n^2 -120n+25n-3000

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

=n+120 ; n-25

=n=-120 ; n=25

But the number of boys can never be negative

•: n=25