Price Increase Calculation
Let the original price of rice be $P$ and the original consumption be $C$. The original expenditure is given by the formula: $ \text{Expenditure} = \text{Price} \times \text{Consumption} $ So, the original expenditure is $E = P \times C$.
New Price and Constant Expenditure
The price of rice is increased by 25%. The new price, $P'$, can be calculated as: $ P' = P + 0.25 \times P = P(1 + 0.25) = 1.25P $ The family wants to keep the expenditure the same. Let the new consumption be $C'$. The new expenditure $E'$ must equal the original expenditure $E$. $ E' = P' \times C' $ $ E = E' \implies P \times C = 1.25P \times C' $
Consumption Decrease Percentage
To find the new consumption $C'$, we rearrange the equation:
$ C' = \frac{P \times C}{1.25P} $ $ C' = \frac{C}{1.25} $ Since $1.25 = \frac{125}{100} = \frac{5}{4}$, we have: $ C' = \frac{C}{5/4} = \frac{4}{5}C = 0.8C $
The decrease in consumption is $C - C'$:
$ \text{Decrease} = C - 0.8C = 0.2C $
To find the percentage decrease in consumption, we use the formula:
$ \text{Percentage Decrease} = \frac{\text{Decrease in Consumption}}{\text{Original Consumption}} \times 100\% $ $ \text{Percentage Decrease} = \frac{0.2C}{C} \times 100\% $ $ \text{Percentage Decrease} = 0.2 \times 100\% = 20\% $ Therefore, the family should decrease its consumption by 20%.
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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 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.
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:
