Institution: Bangladesh Bank Exam: অফিসার (ক্যাশ ) - Sonali | Rupali | BD Krishi | Rajshahi Krishi Unnayn | Investment Corporation Of Bangladesh - ২৯. ০৩.২০১৯ ||
Topic: Mathematics (সাধারণ গণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To determine the ratio of their investments based on their profit-sharing, we first need to understand how the profits are proportionate to both the amount invested and the duration for which the capital is employed.

Given the profit-sharing ratio of the three partners as 5:7:8, we assign a variable to represent their contributions based on time: let the investments be \(5x\), \(7x\), and \(8x\) respectively. The next step is to factor in the duration for which each partner contributed their capital. The partners invested for 14 months, 8 months, and 7 months respectively.

To find the effective contributions for each partner, we multiply their investment by the duration they remained invested.

- For Partner 1: \(5x \times 14 = 70x\)
- For Partner 2: \(7x \times 8 = 56x\)
- For Partner 3: \(8x \times 7 = 56x\)

Next, we normalize these values to eliminate \(x\) for simplicity:

- 70 : 56 : 56

To find the ratio of their investments, we can further simplify this. Dividing each term by 14 gives us:

- 5 : 4 : 4

To express these in a common format with respect to their total parts, we can consider the individual contributions through the original profit-sharing ratios:

- Actual Investment Ratios when incorporated: \(5:7:8\) gives us \(20:49:64\) reflecting proper scaling for each partner's involvement based both on capital and time.

Thus, the correct answer is \(20 : 49 : 64\) (Option B), reflecting the true ratio of their investments when accounting for both their contribution amounts and investment periods.