The price of cooking oil increased by 25%. Find by how much percentage a family must reduce its consumption in order to maintain the same budget.
20%
Solving Cooking Oil Price Increase and Consumption Reduction
This problem asks us to find the percentage reduction in consumption of cooking oil needed to keep the total expenditure constant, given that the price has increased by a certain percentage.
The relationship between Expenditure, Price, and Consumption is given by:
\( \text{Expenditure} = \text{Price} \times \text{Consumption} \)
If the expenditure needs to remain the same, an increase in price must be offset by a decrease in consumption. This is an example of inverse proportionality.
Step-by-Step Calculation for Cooking Oil Consumption
Let's assume some initial values to make the calculation clear. Suppose the initial price of cooking oil is ₹100 per unit, and the family consumes 100 units.
- Initial Price (P₁): ₹100
- Initial Consumption (C₁): 100 units
- Initial Expenditure (E₁): \( P_1 \times C_1 = 100 \times 100 = ₹10000 \)
Now, the price of cooking oil increased by 25%.
- Increase in Price: 25% of ₹100 = \( \frac{25}{100} \times 100 = ₹25 \)
- New Price (P₂): Initial Price + Increase in Price = \( 100 + 25 = ₹125 \)
The family wants to maintain the same budget, meaning the new expenditure (E₂) must be equal to the initial expenditure (E₁).
- Desired New Expenditure (E₂): ₹10000
We know \( E_2 = P_2 \times \text{New Consumption} (C_2) \).
\( 10000 = 125 \times C_2 \)
To find the new consumption (C₂), we rearrange the equation:
\( C_2 = \frac{10000}{125} \)
Let's calculate the new consumption:
\( C_2 = 80 \) units
So, the family must reduce its consumption from 100 units to 80 units to maintain the same budget.
Calculating Percentage Reduction in Consumption
Now, we need to find the percentage decrease in consumption.
- Reduction in Consumption: Initial Consumption (C₁) - New Consumption (C₂) = \( 100 - 80 = 20 \) units
Percentage Reduction in Consumption is calculated as:
\( \text{Percentage Reduction} = \frac{\text{Reduction in Consumption}}{\text{Initial Consumption}} \times 100\% \)
\( \text{Percentage Reduction} = \frac{20}{100} \times 100\% \)
\( \text{Percentage Reduction} = 0.20 \times 100\% \)
\( \text{Percentage Reduction} = 20\% \)
Using a General Formula for Price and Consumption Changes
Alternatively, when the price of an item increases by R%, and the expenditure is to remain constant, the consumption must be reduced by \( \frac{R}{100+R} \times 100 \) %.
In this problem, the price increase (R) is 25%.
\( \text{Percentage Reduction in Consumption} = \frac{25}{100 + 25} \times 100\% \)
\( \text{Percentage Reduction in Consumption} = \frac{25}{125} \times 100\% \)
\( \text{Percentage Reduction in Consumption} = \frac{1}{5} \times 100\% \)
\( \text{Percentage Reduction in Consumption} = 20\% \)
Both methods show that the family must reduce its consumption of cooking oil by 20%.
| Metric | Initial | After Price Increase (Before Consumption Change) | After Consumption Reduction (Desired) |
|---|---|---|---|
| Price (₹) | 100 | 125 (100 + 25% of 100) | 125 |
| Consumption (units) | 100 | 100 (if not reduced) | 80 (Calculated) |
| Expenditure (₹) | 10000 (100 x 100) | 12500 (125 x 100) | 10000 (125 x 80) |
Revision Table: Price and Consumption Basics
| Concept | Relationship | Keeping Expenditure Constant |
|---|---|---|
| Expenditure, Price, Consumption | Expenditure = Price × Consumption | If Expenditure is constant, Price is inversely proportional to Consumption. |
| Price Increase Effect | Higher Price means Higher Expenditure (if Consumption is constant) | To keep Expenditure constant after a Price increase, Consumption must decrease. |
| Price Decrease Effect | Lower Price means Lower Expenditure (if Consumption is constant) | To keep Expenditure constant after a Price decrease, Consumption must increase. |
Additional Information: Percentage Change Calculations
Understanding percentage change is crucial for solving problems like this one involving cooking oil price and consumption.
- Percentage Increase: If a value V₁ increases to V₂, the percentage increase is \( \frac{V_2 - V_1}{V_1} \times 100\% \).
- Percentage Decrease: If a value V₁ decreases to V₂, the percentage decrease is \( \frac{V_1 - V_2}{V_1} \times 100\% \).
- In this problem, the price increased by 25%. If initial price is P, new price is \( P + 0.25P = 1.25P \). The increase is \( 1.25P - P = 0.25P \). Percentage increase is \( \frac{0.25P}{P} \times 100\% = 25\% \).
- We calculated the consumption decreased from 100 units to 80 units. The decrease is \( 100 - 80 = 20 \) units. Percentage decrease is \( \frac{20}{100} \times 100\% = 20\% \). Note that the percentage decrease is calculated with respect to the initial consumption.
Important Questions from Percentage
Radha saves 25% of her income. If her expenditure increases by 20% and her income increases by 29%, then her savings increase by;
The income of A is 45% more than the income of B and the income of C is 60% less than the sum of the incomes of A and B. The income of D is 20% more than that of C. If the difference between the incomes of B and D is Rs. 13200, then the income (in Rs.) of C is:
The population of a city increased by 30% in the first year and decreased by 15% in the next year. If the present population is 11,050 then population 2 years ago was:
The income of A is 30% less than the income of B and the income of B is 137.5% more than that of C. If the income of A is Rs. 28500 less than that of B, then the income (in Rs.) of C is:
Ravi scores 72% marks in examinations. If these are 360 marks, the maximum marks are:
