Find 40% of the fraction?
Statement 1: Numerator of the fraction is 40 % less than its denominator.
Statement 2: Difference between denominator and numerator of the fraction is 4 and denominator of fraction is greater than its denominator.

Options

A. Statement (1) alone is sufficient to answer the question but statement (2) alone is not sufficient to answer the question.
B. Statement (2) alone is sufficient to answer the question but statement (I) alone is not sufficient to answer the question.
C. Both the statements taken together are necessary to answer the question, but neither of the statements alone is sufficient to answer the question.
D. Statements (1) and (2) taken together are not sufficient to answer the question.

Answer

To solve the question "Find 40% of the fraction?" using the provided statements, we will analyze each statement step by step.

### Step 1: Understand the Question
We need to find 40% of a fraction. A fraction is typically represented as \( \frac{numerator}{denominator} \).

### Step 2: Analyze Statement 1
**Statement 1:** The numerator of the fraction is 40% less than its denominator.

Let’s denote:
- Denominator = \( d \)
- Numerator = \( n \)

According to the statement:
\[ n = d - 0.4d = 0.6d \]

Now, the fraction can be expressed as:
\[ \frac{n}{d} = \frac{0.6d}{d} = 0.6 \]

To find 40% of this fraction:
\[ 40\% \text{ of } 0.6 = 0.4 \times 0.6 = 0.24 \]

Thus, from Statement 1, we can conclude that 40% of the fraction is \( 0.24 \).

### Step 3: Analyze Statement 2
**Statement 2:** The difference between the denominator and the numerator of the fraction is 4, and the denominator of the fraction is greater than its numerator.

Let’s denote:
- Denominator = \( d \)
- Numerator = \( n \)

According to the statement:
\[ d - n = 4 \]
This implies:
\[ d = n + 4 \]

Since the denominator is greater than the numerator, we can express the fraction as:
\[ \frac{n}{d} = \frac{n}{n + 4} \]

However, we cannot determine the specific values of \( n \) and \( d \) from this statement alone. The fraction can take many forms depending on the values of \( n \). Thus, we cannot find 40% of the fraction based on this statement alone.

### Conclusion
- **From Statement 1:** We found that 40% of the fraction is \( 0.24 \).
- **From Statement 2:** We concluded that the data is insufficient to determine the fraction.

Therefore, the answer is that Statement 1 alone is sufficient to answer the question, while Statement 2 is not sufficient.

### Final Answer
The correct answer is **Option A**: Statement 1 alone is sufficient, but Statement 2 alone is not sufficient.

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