PREVIOUSLY ASKED IN:
WBPSC Miscellaneous Preliminary 2023
Answer
16 2/3 %
Explanation
To maintain the same overall expenditure when the price of a commodity increases, the percentage reduction in consumption is calculated using the formula: \( \frac{R}{100 + R} \times 100 \). Given the price increase (R) is 20%, the reduction required is \( \frac{20}{120} \times 100 = \frac{1}{6} \times 100 = 16.66\% \) or \( 16\frac{2}{3}\% \).
Key Points
- > Formula for consumption reduction when price increases: \( \frac{R}{100 + R} \times 100 \).
- > Formula for consumption increase when price decreases: \( \frac{R}{100 - R} \times 100 \).
- > Fraction method: 20% = \( \frac{1}{5} \). Price goes from 5 to 6. Consumption must drop from 6 to 5. Drop = 1 out of 6 (\( \frac{1}{6} \)).
- > The fractional equivalent of \( \frac{1}{6} \) is \( 16.66\% \) or \( 16\frac{2}{3}\% \).
- > If the price increased by 25%, consumption would need to drop by 20%.
Additional Information
Percentage Increase-Decrease Table
| Price Increase | Fraction Logic | Consumption Drop |
|---|---|---|
| 20% | \( +\frac{1}{5} \rightarrow -\frac{1}{6} \) | \( 16.66\% \) |
| 25% | \( +\frac{1}{4} \rightarrow -\frac{1}{5} \) | 20% |
| 33.33% | \( +\frac{1}{3} \rightarrow -\frac{1}{4} \) | 25% |
| 50% | \( +\frac{1}{2} \rightarrow -\frac{1}{3} \) | 33.33% |
Memory Tips
- Step Down Rule: Convert the increase to a fraction (e.g., 20% = \( 1/5 \)). Add numerator to denominator (1+5=6) to find the reduction fraction (\( 1/6 \)), which is \( 16.66\% \).