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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- 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
A number p increased by p% of 99 equals 99 increased by 99% of p. What is (p + 51)% of 928 + 72?
Amina saves 16% of her income. Now her income is increased by 20% but she still saves the same amount as before. What is the percentage increase in her expenditure?
What is 12% of 4% of 7% of 2 × 10 6 ?
Vignesh spends 42% of his monthly salary on food, 16% on house rent, 11% on entertainment and 7% on conveyance. But due to some family function, he has to borrow Rs. 12,000 from a money leader to meet the expenses of Rs. 18,000 What is his monthly salary?
If X is 12.25% more than Y. then Y is approximately_____ less than X.
