If Sunita earns `75/4%` more than her boyfriend find the approximate `%` her boyfriend eams less than Sunita
A. `16%`
B. `14%`
C. `25%`
D.`11%`

Options

A. A
B. B
C. C
D. D

Answer

To solve the problem step by step, we need to determine how much less the boyfriend earns compared to Sunita, given that Sunita earns \( \frac{75}{4}\% \) more than him.

### Step 1: Understand the Earnings Relationship
Let the boyfriend's earnings be \( x \). According to the problem, Sunita earns \( \frac{75}{4}\% \) more than her boyfriend. This means:

\[ \text{Sunita's earnings} = x + \left(\frac{75}{4}\% \text{ of } x\right) \]

### Step 2: Convert Percentage to Decimal
To calculate \( \frac{75}{4}\% \) in decimal form, we divide \( 75 \) by \( 4 \) and then convert it to a decimal:

\[ \frac{75}{4} = 18.75 \]

So, \( \frac{75}{4}\% = 0.1875 \).

### Step 3: Calculate Sunita's Earnings
Now, substituting this back into the equation for Sunita's earnings:

\[ \text{Sunita's earnings} = x + (0.1875 \cdot x) = x(1 + 0.1875) = x(1.1875) \]

### Step 4: Find the Percentage Difference
To find out how much less the boyfriend earns compared to Sunita, we can express the difference in earnings as a percentage of Sunita's earnings:

\[ \text{Difference} = \text{Sunita's earnings} - \text{Boyfriend's earnings} = x(1.1875) - x = x(1.1875 - 1) = x(0.1875) \]

Now, the percentage difference compared to Sunita's earnings is:

\[ \text{Percentage difference} = \frac{\text{Difference}}{\text{Sunita's earnings}} \times 100 = \frac{x(0.1875)}{x(1.1875)} \times 100 \]

### Step 5: Simplify the Expression
The \( x \) cancels out:

\[ \text{Percentage difference} = \frac{0.1875}{1.1875} \times 100 \]

Calculating this gives:

\[ \text{Percentage difference} = \frac{0.1875}{1.1875} \approx 0.1579 \times 100 \approx 15.79\% \]

### Step 6: Approximate the Result
Rounding \( 15.79\% \) gives us approximately \( 16\% \).

### Conclusion
Thus, the boyfriend earns approximately \( 16\% \) less than Sunita.

### Final Answer
The correct option is **A. 16%**.

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