Step 1: Understand the problem
- Price increases by 20%.
- Expenditure (price × quantity) should remain the same.
- We need to find the percentage decrease in consumption (quantity).
Step 2: Let original price = 100, original quantity = 100
- Original expenditure = 100 × 100 = 10,000
Step 3: New price
= 100 + 20% of 100 = 120
Step 4: Let new quantity = \(x\)
Since expenditure remains the same:
\(120 \times x = 10,000\)
\(x = \frac{10,000}{120} = 83.33\)
Step 5: Calculate percentage decrease in consumption
Decrease = \(100 - 83.33 = 16.67\)
Percentage decrease = \(\frac{16.67}{100} \times 100 = 16 \frac{2}{3}\)%
Thus, Option (A) 16 \(\frac{2}{3}\)% is correct.