Explanation:

- The profit is divided among Pooja, Seema, and Rutu in the ratio 5 : 7 : 8.

- Their partnership durations are 14, 8, and 7 months, respectively.

- To find the investments’ ratio, multiply the profit share by the inverse of their time periods.

- Calculating:

- Pooja: \(5 \times \frac{1}{14}\)

- Seema: \(7 \times \frac{1}{8}\)

- Rutu: \(8 \times \frac{1}{7}\)

- Simplifying, we get \( \frac{5}{14} : \frac{7}{8} : \frac{8}{7} \).

- Convert to a common scale: \( 5 \times 28 : 7 \times 21 : 8 \times 16 \).

- This results in 140 : 147 : 128, which simplifies to 20 : 49 : 64.

- Hence, the correct answer is:

Option: 1 - 20 : 49 : 64