Question

A class consist of a number of boys whose ages are in ap the common diffrence being 4 mounths if the youngest boy is just 8 years old and if the sum of the ages is 168 years . Find the numbers of boys

Answer 1

8 would be the first term of the A.P, next term would be 8+(4/12) = 25/3
Therefore the A.P would be 8,(25/3),(26/3),...........
a1=8, common difference = 1/3
an=a+(n-1)d
   =8+(n-1)*1/3
   =8+(n-1)/3
   =(24+n-1)/3
  =(23+n)/3

Sn=n/2*(a+an)
168=n/2*[8+(23+n)/3]
168*2=n[(24+23+n)/3]
336*3=n(47+n)
1008=n2+47n
n2+47n-1008=0
n2+63n-16n-1008=0
n(n+63)-16(n+63)=0
(n-16)(n+63)=0
Therefore n=16 or -63. So there are 16 boys in the class

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