Question

A class consists of a number of boys whose ages are in A.P. the common difference being four months. If the youngest boy is just eight years old and if the sum of the ages is $168$ years, find the number of boys.

Answer 1

Here,

$Firstterm=ageofyoungestboy=8=a$

$a=8$

$d=4months=\frac{4}{12}years=\frac{1}{3}years$

$S_n=n\cdot \frac{2a+(n-1)d}{2}=168$

$\Rightarrow n\cdot \frac{16+(n-1)\frac{1}{3}}{2}=168$

$\Rightarrow n\cdot \frac{48+(n-1)1}{2\cdot 3}=168$

$\Rightarrow 48n+n^2-n=6\times 168$

$\Rightarrow n^2+47n-1008=0$

$\Rightarrow (n-16)(n+63)=0$

$n=16or-63$

$\because n\ge 0$, because it is no. of persons

$\therefore n=16$

$Theno.ofpersonsis16$