Explanation:

To solve this problem, follow these steps:

- Initial Situation: The family initially consumed 18.4 kg of sugar.

- Price Increase: The price of sugar increased by 28%.

- New Expenditure: The family wants the expenditure to be only 12% more than before.

Mathematical Calculation:

1. Let the initial price per kg of sugar be \( p \).

2. Initial expenditure = \( 18.4 \times p \).

3. New price per kg = \( p + 0.28p = 1.28p \).

4. Let new consumption be \( x \) kg.

5. New expenditure = \( x \times 1.28p \).

6. New expenditure is 12% more, so \( 1.12 \times 18.4p = x \times 1.28p \).

7. Solve for \( x \):

\( 1.12 \times 18.4 = 1.28x \).

\( x = \frac{1.12 \times 18.4}{1.28} \).

\( x \approx 16.1 \).

- Options:

1. 16.6 kg

2. 16.1 kg

3. 15.75 kg

4. 15.8 kg

- Highlight Correct Answer:

- Option 2: 16.1 kg is correct.

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