When the price of sugar increased by 28%, a family reduced its consumption per month such that the expenditure on sugar was only 12% more than the earlier one. If the family consumed 18.4 kg sugar per month earlier, then what is its new consumption of sugar per month?

Options

A. 16.6 kg
B. 16.1 kg
C. 15.75 kg
D. 15.8 kg

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the initial expenditure on sugar.
The initial consumption of sugar is given as 18.4 kg per month. Let the price of sugar per kg be \( x \).

Thus, the initial expenditure on sugar can be calculated as:
\[ \text{Initial Expenditure} = \text{Consumption} \times \text{Price} = 18.4 \times x \]

### Step 2: Calculate the new price of sugar after the increase.
The price of sugar increases by 28%. Therefore, the new price of sugar will be:
\[ \text{New Price} = x + 0.28x = 1.28x \]

### Step 3: Determine the new expenditure on sugar.
The problem states that the new expenditure is 12% more than the initial expenditure. Therefore, the new expenditure can be calculated as:
\[ \text{New Expenditure} = \text{Initial Expenditure} + 0.12 \times \text{Initial Expenditure} = 1.12 \times \text{Initial Expenditure} \]
Substituting the initial expenditure:
\[ \text{New Expenditure} = 1.12 \times (18.4 \times x) = 20.608x \]

### Step 4: Set up the equation for new consumption.
Let the new consumption of sugar be \( y \) kg. The new expenditure can also be expressed as:
\[ \text{New Expenditure} = \text{New Price} \times \text{New Consumption} = (1.28x) \times y \]
Setting the two expressions for new expenditure equal:
\[ 20.608x = 1.28x \times y \]

### Step 5: Solve for the new consumption \( y \).
To isolate \( y \), divide both sides by \( 1.28x \):
\[ y = \frac{20.608x}{1.28x} \]
The \( x \) cancels out:
\[ y = \frac{20.608}{1.28} \]
Calculating the right side:
\[ y = 16.1 \]

### Conclusion:
The new consumption of sugar per month is \( 16.1 \) kg.