If the price of milk is increased by `35%` by how much a lady must reduced her consumption so that her expenditure is increased only by `8%` .

Answer

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

### Step 1: Define Variables
Let the original price of milk be \( P \) per liter and the original consumption be \( C \) liters. Therefore, the original expenditure \( E \) can be expressed as:
\[ E = P \times C \]

### Step 2: Calculate the New Price
If the price of milk is increased by \( 35\% \), the new price \( P' \) will be:
\[ P' = P + 0.35P = 1.35P \]

### Step 3: Calculate the New Expenditure
The lady wants her expenditure to increase by \( 8\% \). Therefore, the new expenditure \( E' \) will be:
\[ E' = E + 0.08E = 1.08E \]
Substituting the expression for \( E \):
\[ E' = 1.08(P \times C) = 1.08PC \]

### Step 4: Set Up the Equation for New Consumption
Let the new consumption be \( C' \) liters. The new expenditure can also be expressed as:
\[ E' = P' \times C' = 1.35P \times C' \]
Setting the two expressions for \( E' \) equal gives:
\[ 1.08PC = 1.35P \times C' \]

### Step 5: Simplify the Equation
We can cancel \( P \) from both sides (assuming \( P \neq 0 \)):
\[ 1.08C = 1.35C' \]

### Step 6: Solve for New Consumption
Rearranging the equation to find \( C' \):
\[ C' = \frac{1.08C}{1.35} \]
Calculating \( C' \):
\[ C' = \frac{1.08}{1.35}C \]
\[ C' = 0.8C \]

### Step 7: Calculate the Reduction in Consumption
The reduction in consumption \( R \) can be calculated as:
\[ R = C - C' = C - 0.8C = 0.2C \]

### Step 8: Express Reduction as a Percentage
To find the percentage reduction in consumption:
\[ \text{Percentage Reduction} = \left( \frac{R}{C} \right) \times 100 = \left( \frac{0.2C}{C} \right) \times 100 = 20\% \]

### Final Answer
The lady must reduce her consumption by \( 20\% \).

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