If A's income is 150% more than that of B, then how much per cent is B's income less than that of A?

Options

A. `50%`
B. `60%`
C. `12.5%`
D. `25%`

Answer

To solve the problem step by step, let's break it down:

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

### Step 2: Calculate A's Income
Since A's income is 150% more than B's income, we can express A's income as:
\[ A = B + 150\% \text{ of } B \]
This can be rewritten as:
\[ A = X + \frac{150}{100} \times X \]
\[ A = X + 1.5X = 2.5X \]

### Step 3: Find the Difference in Income
Now, we need to find how much less B's income is compared to A's income. The difference in their incomes is:
\[ \text{Difference} = A - B = 2.5X - X = 1.5X \]

### Step 4: Calculate the Percentage Difference
To find out how much percent B's income is less than A's income, we use the formula:
\[ \text{Percentage} = \left( \frac{\text{Difference}}{A} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage} = \left( \frac{1.5X}{2.5X} \right) \times 100 \]
The \( X \) cancels out:
\[ \text{Percentage} = \left( \frac{1.5}{2.5} \right) \times 100 \]

### Step 5: Simplify the Fraction
Now, simplify \( \frac{1.5}{2.5} \):
\[ \frac{1.5}{2.5} = \frac{15}{25} = \frac{3}{5} \]
Thus,
\[ \text{Percentage} = \left( \frac{3}{5} \right) \times 100 = 60\% \]

### Conclusion
Therefore, B's income is 60% less than A's income.

---