Answer
The number of people in the group is $4$.
Work Step by Step
If the group number is $x$ person, the cost per person is $120,000/x$.
By increasing the group by one person, the number will be $x+1$ and the cost per person will be $120000/(x+1)$.
The new contribution is $6000$ less than the original one per-person.
$ 120000/(x+1) = 120000/x - 6000$
$\Rrightarrow (120000/x)-120000/(x+1)=6000$
$\Rrightarrow120000[1/x - 1/(x+1)]=6000$
$\Rrightarrow20[1/x - 1/(x+1)] = 1$
$\Rrightarrow20[(x+1-x)/x(x+1)]=1$
$\Rrightarrow20[1/x(x+1)]=1$
$\Rrightarrow x(x+1)=20$
$\Rrightarrow x^2+x-20=0$
$\Rrightarrow(x+5)(x-4)=0$
$\Rrightarrow x=-5\hspace{0.3cm}{\color{red}{reject}}$
or $x=4$
The number of people in the group is $4$.
