Groundnut oil is now being sold at Rs. 27 per kg . During last month its cost was Rs. 24 per kg . Find by how much % a family should reduce its consumption , so as to keep the expenditure same.

Options

A. `11(1)/(9)%`
B. `11(1)/(9)%`
C. `11(9)/(10)%`
D. `9(1)/(10)%`

Explanation

To solve the problem of how much a family should reduce its consumption of groundnut oil to keep the expenditure the same after the price increase, we can follow these steps:

### Step 1: Identify the initial and new prices
- Initial price of groundnut oil = Rs. 24 per kg
- New price of groundnut oil = Rs. 27 per kg

### Step 2: Calculate the change in price
- Change in price = New price - Initial price
- Change in price = 27 - 24 = Rs. 3

### Step 3: Calculate the percentage change in price
- Percentage change in price = (Change in price / Initial price) × 100
- Percentage change in price = (3 / 24) × 100
- Percentage change in price = (1 / 8) × 100 = 12.5%

### Step 4: Use the formula to find the reduction in consumption
To maintain the same expenditure, the formula to find the required reduction in consumption is:
\[ \text{Required Reduction in Consumption} = \frac{\text{Percentage Change in Price}}{\text{Percentage Change in Price} + 100} \times 100 \]

### Step 5: Substitute the values into the formula
- Required Reduction in Consumption = \(\frac{12.5}{12.5 + 100} \times 100\)
- Required Reduction in Consumption = \(\frac{12.5}{112.5} \times 100\)

### Step 6: Calculate the required reduction
- Required Reduction in Consumption = \(\frac{12.5 \times 100}{112.5}\)
- Required Reduction in Consumption = \(\frac{1250}{112.5} \approx 11.11\%\)

### Step 7: Final answer
The family should reduce its consumption of groundnut oil by approximately **11.11%** to keep the expenditure the same.

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