If A's income is 40% less than that of B. How much percent B's income is more than that of A?

Question

Accepted Answer

To determine how much percent B's income is more than that of A, we start by understanding the relationship between their incomes. According to the question, A's income is 40% less than B's income. Let's break this down step by step:

1. **Understanding the Income Relationship:**
   - Let B's income be represented as 100 units (since we are dealing with percentages, using 100 makes calculations straightforward).
   - A's income is 40% less than B's income. Therefore, A's income is 60% of B's income (100 - 40 = 60).

2. **Calculating the Difference:**
   - The difference in income between B and A is 100 units (B's income) - 60 units (A's income) = 40 units.

3. **Calculating the Percentage Increase:**
   - To find out how much percent B's income is more than A's income, we calculate the percentage increase from A's income to B's income.
   - The formula for percentage increase is: $\text{Percentage Increase} = \left(\frac{\text{Difference}}{\text{Original Value}}\right) \times 100\%$.
   - Here, the original value is A's income, which is 60 units.
   - So, the percentage increase is $\left(\frac{40}{60}\right) \times 100\% = \frac{2}{3} \times 100\% = 66\frac{2}{3}\%$.

4. **Conclusion:**
   - Therefore, B's income is 66$\frac{2}{3}\%$ more than A's income, which corresponds to Option 4.

**Explanation of Incorrect Options:**

- **Option 1 (25%):** This would imply that B's income is only 25% more than A's income. However, as calculated, the actual percentage increase is much higher at 66$\frac{2}{3}\%$.

- **Option 2 (40%):** This option might confuse the percentage difference with the percentage by which A's income is less than B's. However, the question asks for how much more B's income is compared to A's, which is not 40%.

- **Option 3 (33$\frac{1}{3}\%$):** This option suggests that B's income is 33$\frac{1}{3}\%$ more than A's income. This is incorrect as the calculated percentage increase is 66$\frac{2}{3}\%$.

In conclusion, Option 4 is the correct answer because it accurately reflects the percentage by which B's income is more than A's income, based on the given relationship.