Question

Q 24 very hard question

Answer 1

here is ur answer......

Answer 2

The age of the youngest boy (a) = 8 years.
Common difference of participants (d)
= 4 months = 4/12 years = 1/3.
Sum of the ages of all the participants ( Sn ) = 168.

So,
Sn = n/2 (2a + [n-1]d)
168 = n/2 ( 2*8 + [n-1]1/3)
336 = n (16+ n/3 - 1/3)
336 = n (n/3 + 47/3)
336 = n^2/3 + 47n/
Multiplying by 3 on both sides

1008 = n^2 + 47n
n^2 + 47n - 1008 = 0
n^2 + 63n - 16n - 1008 = 0
n (n+ 63) - 16 (n+ 63)= 0

Therefore
n= -63 , 16.
However the number of terms cannot be negative so n = 16.
Now,

The eldest participant (An) = ?

An = a + ( n - 1)d
A 16 = 8 + 15 * 1/3
A16 = 8 + 5 = 13
A16 = age of the eldest participant = 13 years.