If A's salary is 50% more than that of B, then B's salary is less than A's by

Options

A. 0.33
B. `40 1/3%`
C. `45 1/3%`
D. `33 1/3%`

Answer

To solve the problem step by step, we will analyze the information given about the salaries of A and B.

### Step 1: Define the Salaries
Let B's salary be denoted as \( B \).

### Step 2: Calculate A's Salary
According to the problem, A's salary is 50% more than B's salary. This can be expressed mathematically as:
\[ A = B + 0.5B = 1.5B \]

### Step 3: Express A's Salary in Fraction Form
We can also express A's salary in terms of a fraction:
\[ A = \frac{3}{2}B \]

### Step 4: Find the Difference Between A's and B's Salaries
Now, we need to find how much less B's salary is compared to A's salary:
\[ \text{Difference} = A - B = \frac{3}{2}B - B \]
This simplifies to:
\[ \text{Difference} = \frac{3}{2}B - \frac{2}{2}B = \frac{1}{2}B \]

### Step 5: Calculate the Percentage Difference
To find out how much less B's salary is than A's salary in percentage terms, we use the formula:
\[ \text{Percentage Difference} = \left(\frac{\text{Difference}}{A}\right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Difference} = \left(\frac{\frac{1}{2}B}{\frac{3}{2}B}\right) \times 100 \]
This simplifies to:
\[ \text{Percentage Difference} = \left(\frac{1}{2} \div \frac{3}{2}\right) \times 100 = \left(\frac{1}{2} \times \frac{2}{3}\right) \times 100 = \frac{1}{3} \times 100 = 33.33\% \]

### Final Answer
B's salary is less than A's salary by \( 33.33\% \).

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