Question

the minimum age of children to be eligible to participate in competition is 8 years it is observed that age of youngest boy was 8 years and the age of rest of participant have C.D of 4 months if sum of Ages of all participants is 168 years find the age of eldest participated

Answer 1

Answer:

13 year

Step-by-step explanation:

Age of youngest = 8 years = 8*12 = 96 months

a = 96 months

Common difference = 4 months

d = 4 months

let say n students  

age of eldest = a + (n-1)d  

L = 96 + (n-1)4 = 92 + 4n  

Sum = (n/2)(a + L)

Sum = 168 Years = 168 * 12 months

168* 12 = (n/2) ( 96 + 92 + 4n)

168*12 = (n/2)(188 + 4n)

168*12 = n ( 94 + 2n)

168*6 = n(47 + n)     (dividing by 2 both sides)

n^2 + 47 n  - 1008 = 0

n^2 + 63n - 16n - 1008 = 0

(n+63)(n-16) = 0

n = 16   as n can not be negative

L = 92 + 4n

L = 92 + 4*16

L = 92 +64

L = 156 months

L = 13 Years

so age of eldest participant = 13 Year