The income of A is 30% more than the income of B. How much percent is B's income less than A's?
Understand the Problem
The question is asking to calculate how much percent B's income is less than A's income, given that A's income is 30% more than B's income.
Answer
$23.08\%$
Answer for screen readers
B's income is approximately $23.08%$ less than A's income.
Steps to Solve
- Define the incomes of A and B
Let B's income be represented as $B$. Since A's income is 30% more than B's income, we can express A's income as: $$ A = B + 0.3B = 1.3B $$
- Calculate the difference in incomes
To find out how much less B's income is compared to A's, we calculate the difference: $$ \text{Difference} = A - B = 1.3B - B = 0.3B $$
- Find the percentage difference
To determine how much percent B's income is less than A's income, we use the formula: $$ \text{Percentage difference} = \left( \frac{\text{Difference}}{A} \right) \times 100 $$ Substituting the values: $$ \text{Percentage difference} = \left( \frac{0.3B}{1.3B} \right) \times 100 $$
- Simplify the expression
The $B$ in the numerator and denominator cancels out: $$ \text{Percentage difference} = \left( \frac{0.3}{1.3} \right) \times 100 $$
- Calculate the percentage
Now, we compute: $$ \frac{0.3}{1.3} \approx 0.2308 $$ Therefore: $$ \text{Percentage difference} \approx 23.08% $$
B's income is approximately $23.08%$ less than A's income.
More Information
This calculation shows the relationship between two incomes where one is a fixed percentage greater than the other. Understanding percentage differences is crucial in both financial and mathematical contexts.
Tips
- Forgetting to convert the percentage into a fraction before performing calculations.
- Not canceling out like terms, leading to incorrect results.
- Misunderstanding the difference between "more than" and "less than" when setting up the equations.
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