Price of milk has increased by 20%. To keep the expenditure unchanged, the present consumption is to be reduced by-

Options

A. `16(2/3)%`
B. `20%`
C. `18%`
D. `10%`

Answer

To solve the problem of how much the present consumption of milk needs to be reduced to keep the expenditure unchanged after a 20% increase in price, we can follow these steps:

### Step 1: Understand the Increase in Price
The price of milk has increased by 20%. This means if the original price is P, the new price becomes:
\[ \text{New Price} = P + 0.20P = 1.20P \]

### Step 2: Define the Expenditure
Let’s assume the initial consumption of milk is C liters. The initial expenditure (E) on milk can be calculated as:
\[ E = \text{Price} \times \text{Consumption} = P \times C \]

### Step 3: Calculate New Expenditure
After the price increase, if the consumption is reduced to C', the new expenditure will be:
\[ E' = \text{New Price} \times \text{New Consumption} = 1.20P \times C' \]

### Step 4: Set Expenditures Equal
To keep the expenditure unchanged, we set the initial expenditure equal to the new expenditure:
\[ P \times C = 1.20P \times C' \]

### Step 5: Simplify the Equation
We can cancel P from both sides (assuming P is not zero):
\[ C = 1.20 \times C' \]

### Step 6: Solve for C'
Rearranging gives us:
\[ C' = \frac{C}{1.20} \]

### Step 7: Calculate the Reduction in Consumption
To find the reduction in consumption, we need to calculate:
\[ \text{Reduction} = C - C' \]
Substituting C' from the previous step:
\[ \text{Reduction} = C - \frac{C}{1.20} \]
\[ \text{Reduction} = C \left(1 - \frac{1}{1.20}\right) \]
\[ \text{Reduction} = C \left(1 - \frac{5}{6}\right) = C \left(\frac{1}{6}\right) \]

### Step 8: Calculate the Percentage Reduction
To find the percentage reduction in consumption:
\[ \text{Percentage Reduction} = \left(\frac{\text{Reduction}}{C}\right) \times 100 \]
Substituting the reduction:
\[ \text{Percentage Reduction} = \left(\frac{\frac{C}{6}}{C}\right) \times 100 = \frac{1}{6} \times 100 = 16.67\% \]

### Step 9: Final Answer
Thus, the present consumption is to be reduced by approximately 16.67%, which can also be expressed as \( 16 \frac{2}{3} \% \).