Explanation:

To find the ratio of investments of A, B, and C, we need to divide the ratio of their profits by the ratio of their time periods:

- Consider their time periods as 3x, 2x, and 7x respectively.

- Their profit ratio is given as 4:3:14.

Investment is directly proportional to profit and inversely proportional to time. Thus, the investment ratio will be:

- A's investment: 4 / 3 = 4/3

- B's investment: 3 / 2 = 3/2

- C's investment: 14 / 7 = 2

To find the common scale, multiply each fraction by 6 (common multiple of denominators 3 and 2):

- A's investment: (4/3) * 6 = 8

- B's investment: (3/2) * 6 = 9

- C's investment: 2 * 6 = 12

Thus, the investment ratio is 8:9:12.

- Option 3: 8:9:12 is the correct ratio.

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