Amit and Ben started a partnership by investing Rs.3600 and Rs.4500, respectively. Amit's investment period is 'x' months, while Ben's investment period is '(x + 3)' months. The combined profit earned by them is Rs.4100. Additionally, one-third of the difference between Amit's and Ben's profit shares is Rs.300. If Amit's share of the profit is less than Ben's, determine the duration of Ben's investment period.