Explanation:

- The initial investment ratio of Suresh, Dinesh, and Ramesh is 3:6:8.

- The increase in investments is 5% for Suresh, 15% for Dinesh, and 20% for Ramesh.

- The updated investments are calculated as follows:

- Suresh: 3 * 1.05 = 3.15

- Dinesh: 6 * 1.15 = 6.9

- Ramesh: 8 * 1.20 = 9.6

- New profit ratio is based on the updated investments: 3.15 : 6.9 : 9.6.

- To simplify, multiply each by 20 (to clear decimals):

- Suresh: 3.15 * 20 = 63

- Dinesh: 6.9 * 20 = 138

- Ramesh: 9.6 * 20 = 192

- Calculating the simplest form of 63:138:192 gives us the ratio 21:46:64.

- Therefore, the correct option is Option 3: 21:46:64.

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