What is the percentage decrease required?
Understanding the Percentage Change Problem
The question asks us to find the percentage decrease needed to revert a value back to its original amount after it was initially increased by 30%. We need to calculate this unknown percentage decrease.
Step-by-Step Calculation
- Assume an Original Value: Let the original value be $100$. This makes percentage calculations easier.
- Calculate the Value After 30% Increase: The increase is $30\%$ of $100$. Increase = $\frac{30}{100} \times 100 = 30$. The new value is $100 + 30 = 130$. Alternatively, using a multiplier: $100 \times (1 + 0.30) = 100 \times 1.30 = 130$.
- Set up the Decrease Calculation: Let the required percentage decrease be $x\%$. This decrease is applied to the new value ($130$) to return to the original value ($100$). The decrease amount is $x\%$ of $130$, which is $\frac{x}{100} \times 130$. The equation is: $130 - (\frac{x}{100} \times 130) = 100$.
- Solve for the Percentage Decrease ($x$): Rearrange the equation: $130 - 100 = \frac{130x}{100}$ $30 = \frac{130x}{100}$ Multiply both sides by $100$: $30 \times 100 = 130x$ $3000 = 130x$ Solve for $x$: $x = \frac{3000}{130} = \frac{300}{13}$
- Calculate the Final Percentage: $x \approx 23.0769...$ Rounding to two decimal places gives $23.08\%$.
Therefore, a decrease of approximately 23.08% is required to return the value to its original amount.
Similar Questions
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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:
