To calculate the percentage change in price for maize based on the supply schedule provided, we need to follow a systematic approach. Let's break it down step-by-step.
Step 1: Identify the Prices
From the table, we have two prices for maize:
- Initial Price (P1) = 16
- New Price (P2) = 24
Step 2: Calculate the Change in Price
The change in price (ΔP) can be calculated using the formula:
[
\Delta P = P2 - P1
]
Substituting the values:
[
\Delta P = 24 - 16 = 8
]
Step 3: Calculate the Percentage Change in Price
The percentage change in price can be calculated using the formula:
[
\text{Percentage Change} = \left( \frac{\Delta P}{P1} \right) \times 100
]
Substituting the values we have:
[
\text{Percentage Change} = \left( \frac{8}{16} \right) \times 100
]
Calculating this gives:
[
\text{Percentage Change} = 0.5 \times 100 = 50\%
]
Conclusion
The percentage change in price for maize is
50.0%. Therefore, the correct option is
C. 50.0%.
Explanation of Other Options
-
A. 8.0%: This option represents the absolute change in price (8) as a percentage of the new price (24), which is incorrect for calculating the percentage change from the original price.
-
B. 33.3%: This option does not correspond to any calculation based on the given prices. It may arise from a misunderstanding of the percentage change formula or incorrect values.
-
D. 66.7%: This option is also incorrect. It could be mistakenly calculated by using the new price as the base instead of the original price, leading to an inflated percentage.
Common Pitfalls
- Using the wrong base price: Always use the original price (P1) when calculating percentage change.
- Confusing absolute change with percentage change: Remember that the percentage change is a ratio of the change to the original value, not just the change itself.
Revision Summary
- The percentage change in price is calculated using the formula: (\left( \frac{\Delta P}{P1} \right) \times 100).
- Always use the original price as the base for percentage calculations.
- The correct answer for the percentage change in price for maize is 50.0% (Option C).
- Be cautious of common mistakes, such as using the new price as the base or confusing absolute change with percentage change.