Question

the minimum age of children to participate in a competition is 8 yrs.it is observed that the age of youngest boy was 8 yrs and the ages of the rest are common diff of 4 MONTHS .if the sum of ages of all the participants is 168 yrs,find the age of eldest participant in this comp.

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)

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