Given that, $1\;\text{person} = 120\;\text{days} \Rightarrow 120\;\text{persons} = 1\;\text{day}$
Let, the number of days are required to complete the job be $n$.
$1+2+3+4+5+ \ldots + n = 120 \quad [\because \text{Efficiency are equal}]$
$\Rightarrow \frac{n(n+1)}{2} = 120$
$\Rightarrow n^{2} + n = 240$
$\Rightarrow n^{2} + n – 240 = 0$
$\Rightarrow n^{2} + 16n – 15n – 240 = 0$
$\Rightarrow n(n+16) -15(n+16) = 0$
$\Rightarrow (n+16)(n-15) = 0$
$\Rightarrow n = 15, n = -16\;(\text{The number of days can’t be negative})$
$\Rightarrow \boxed{n = 15}$
$\therefore$ The number of days is required to complete the job $ = 15$ days.
Correct Answer $: \text{A}$