Explanation:

- Amit started his business with Rs. 80,000.

- Sumit joined with Rs. 48,000 after a few months.

- The profit sharing ratio is 5:1 between Amit and Sumit.

- To find when Sumit joined, consider the investment time proportion needed to achieve the 5:1 profit ratio.

- Amit's money was invested for 12 months, which totals 80,000 x 12 = 960,000.

- Let Sumit join after x months, leaving him in business for (12 - x) months.

- Sumit's investment for (12 - x) months: 48,000 x (12 - x).

- Ratio of investments: (48,000 x (12 - x)) / 960,000 = 1/5.

- Solving gives x = 4, which means Sumit joined after 8 months.

- 'Correct Answer is Option 5: 8 Months '