Solving the Percentage Error Calculation
This problem involves calculating the difference between a mistaken calculation and the intended correct calculation, expressed as a percentage.
Step-by-Step Solution
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Assume an Initial Value: Let the original number be $100$. This makes percentage calculations straightforward.
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Calculate the Mistaken Value: The number was mistakenly increased by $25\%$. Calculation: $100 \times (1 + 0.25) = 100 \times 1.25 = 125$. The mistaken result is $125$.
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Calculate the Correct Value: The number should have been decreased by $20\%$. Calculation: $100 \times (1 - 0.20) = 100 \times 0.80 = 80$. The correct value is $80$.
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Find the Difference: Calculate the difference between the mistaken result and the correct value. Difference: $125 - 80 = 45$.
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Calculate the Percentage Difference: Express this difference as a percentage of the correct value ($80$). Percentage Increase $= \frac{\text{Mistaken Value} - \text{Correct Value}}{\text{Correct Value}} \times 100$ Percentage Increase $= \frac{45}{80} \times 100$ Percentage Increase $= \frac{9}{16} \times 100 = 0.5625 \times 100 = 56.25\%$.
The final result is $56.25\%$ more than the correct value.
Similar Questions
- A student's marks in Mathematics were 20% more than in Physics. If he scored 72 in Physics, how many marks did he score in Mathematics?
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- A person spends 80% of his income and saves ₹2000. What is his income?
- The population of a village increases by 8% annually. If the current population is 58,320, what was it two years ago (approx)?
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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:
