Explanation:

To solve the problem, let’s define the variables:

- Let the amount lent at 7% be X.

- The amount lent at 9% will be 2550 - X (since the total sum is 2550).

We know:

- Interest from the 7% amount for 4 years = \(X \times 7 \times 4 / 100 = 0.28X\).

- Interest from the 9% amount for 4 years = \((2550 - X) \times 9 \times 4 / 100 = 0.36 \times (2550 - X)\).

The total interest from both amounts after 4 years is 800:

$$0.28X + 0.36(2550 - X) = 800$$

Simplifying this equation:

- Solve for X and find:

- 0.28X + 918 - 0.36X = 800

- -0.08X = -118

- X = 1475

The amount lent at 9% = 2550 - 1475 = 1075.

- Ratio of money lent at 7% to 9%:

- \(\text{1475:1075}\)

- This simplifies to \(59:43\).

So, option 4 (59 : 43) is correct.

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