The price of cooking oil has increased by `25%`. The percentage of reduction that a family shoulf effect in the use of cooking oil so as not to increase the expenditure on this account is--

Options

A. `15%`
B. `20%`
C. `25%`
D. `30%`

Answer

To solve the problem of how much a family should reduce their consumption of cooking oil to maintain the same expenditure after a 25% increase in price, we can follow these steps:

### Step 1: Understand the relationship between price, consumption, and expenditure.
Expenditure (E) is calculated as:
\[ E = \text{Price} \times \text{Consumption} \]

### Step 2: Define the initial price and the new price after the increase.
Let's assume the initial price of cooking oil is \( P = 100 \) (this is a convenient choice for calculation). After a 25% increase, the new price becomes:
\[ \text{New Price} = P + (25\% \text{ of } P) = 100 + 25 = 125 \]

### Step 3: Set up the equation for expenditure before and after the price increase.
Let the initial consumption be \( C \). The initial expenditure can be expressed as:
\[ E = P \times C = 100 \times C \]

After the price increase, if the consumption is reduced to \( C' \), the new expenditure will be:
\[ E' = \text{New Price} \times C' = 125 \times C' \]

### Step 4: Equate the initial and new expenditure to find the new consumption.
To keep the expenditure the same, we set \( E = E' \):
\[ 100 \times C = 125 \times C' \]

### Step 5: Solve for the new consumption \( C' \).
Rearranging the equation gives:
\[ C' = \frac{100}{125} \times C = \frac{4}{5} \times C = 0.8C \]

### Step 6: Calculate the reduction in consumption.
The reduction in consumption is:
\[ \text{Reduction} = C - C' = C - 0.8C = 0.2C \]

### Step 7: Find the percentage reduction in consumption.
To find the percentage reduction, we use the formula:
\[ \text{Percentage Reduction} = \left(\frac{\text{Reduction}}{C}\right) \times 100\% = \left(\frac{0.2C}{C}\right) \times 100\% = 20\% \]

### Conclusion
Thus, the family should reduce their consumption of cooking oil by **20%** to maintain the same expenditure after the price increase.

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