we can see that,

On Day 1, the person works alone. So, work done on Day 1 = 1/120

Next day, another person joins him, Work done on Day 2 = 2/120

And so on, until the final day

So, sum total of work done = 1/120 + 2/120 +………+ n/120 = 1

(1/120) (1 + 2+3+……+n) = 1

(1/120) [n(n+1)/2] = 1 (Sum of n positive integers)

On solving, we get n = 15.