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

Answer

To solve the problem step by step, we need to determine how much percent B's income is more than A's income, given that A's income is 40% less than B's income.

### Step 1: Define B's Income
Let B's income be represented as \( B \).

### Step 2: Calculate A's Income
Since A's income is 40% less than B's income, we can express A's income as:
\[ A = B - 0.4B = 0.6B \]
This means A's income is 60% of B's income.

### Step 3: Determine the Difference in Income
Now, we need to find out how much more B's income is compared to A's income. The difference in income is:
\[ B - A = B - 0.6B = 0.4B \]

### Step 4: Calculate the Percentage Increase
To find out how much percent B's income is more than A's income, we use the formula for percentage increase:
\[ \text{Percentage Increase} = \left( \frac{\text{Difference}}{\text{A's Income}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Increase} = \left( \frac{0.4B}{0.6B} \right) \times 100 \]

### Step 5: Simplify the Expression
The \( B \) cancels out:
\[ \text{Percentage Increase} = \left( \frac{0.4}{0.6} \right) \times 100 = \left( \frac{4}{6} \right) \times 100 = \left( \frac{2}{3} \right) \times 100 \]

### Step 6: Calculate the Final Result
Now, calculating \( \frac{2}{3} \times 100 \):
\[ \text{Percentage Increase} = \frac{200}{3} \approx 66.67\% \]
Thus, B's income is \( 66 \frac{2}{3}\% \) more than A's income.

### Final Answer
B's income is \( 66 \frac{2}{3}\% \) more than A's income.

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