Question

a picnic group for Shimla consists of students whose ages are in AP the common difference being 3 months if the youngest student Neeraj is just 12 years old the sum of Ages of all students is 375 years find the number of students in a group

Answer 1

let n be the number of students

common difference d = 3 months = 3/12 = 1/4 years

age of youngest = 12 years

sum of ages = 375 years

n/2 ( 2a + (n-1)d) = 375

n(2(12) + (n-1)1/4 ) = 750

n(24*4 + (n-1)) = 750 *4 = 3000

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

96n + n^2 - n = 3000

n^2 + 95n - 3000 = 0

factorising and solving

n^2 + 120n - 25n - 3000 =0

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

so n = -120 or n = 25

so n is number of students it cant be negative so n = 25