Explanation:

- Let's call the smaller number "x" and the larger number "y".

- The first condition states: 65% of x = 45% of y.

- This can be translated to the formula: 0.65x = 0.45y.

- According to the second condition, x + y = 2574.

- Solve for y: From 0.65x = 0.45y, we get x = 0.45y / 0.65, which simplifies to x = 9y / 13.

- Substitute x = 9y / 13 into the equation x + y = 2574:

- (9y / 13) + y = 2574.

- Solve for y: (9y + 13y) / 13 = 2574.

- 22y = 2574 * 13.

- 22y = 33462.

- y = 33462 / 22.

- y = 1521.

- Therefore, the larger number is 1521.

Option 3: 1521 is the correct answer.

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