The following questions are accompanied by two statements (I) and (II). You have to determine which statements(s) is/are sufficient/ necessary to answer the questions.
Find profit share of C at the end of the year.
I. A,B & C invested in a partnership business in the ratio 12:11:18 for 1 year. Difference between profit share of A & C at the end of the year is Rs7800.
II C, D&F invested in a partnership business in the ratio 54:8:2 and period of investment of C, D & F is 6 months, 4 months & 12 months. Profit share of F at the end of the year is Rs.18720.

Options

A. Statement (I) alone is sufficient to answer the question but statement (II) alone is not sufficient to answer the question
B. Statement (II) 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. Either statement (I) or statement (II) by itself is sufficient to answer the question.

Answer

To determine the profit share of C at the end of the year, we will analyze the two statements provided and see if either or both are sufficient to answer the question.

### Step 1: Analyze Statement I
Statement I states that A, B, and C invested in a partnership business in the ratio 12:11:18 for 1 year. The difference between the profit share of A and C at the end of the year is Rs. 7800.

1. **Calculate the profit share ratio**:
- The profit share ratio of A, B, and C is 12:11:18.
- Let the total profit be represented in terms of units: A's share = 12x, B's share = 11x, C's share = 18x.

2. **Find the difference between A's and C's profit shares**:
- The difference between A's and C's profit shares is given as:
\[ C's \, share - A's \, share = 18x - 12x = 6x \]
- According to the statement, this difference equals Rs. 7800:
\[ 6x = 7800 \]
- Solving for x:
\[ x = \frac{7800}{6} = 1300 \]

3. **Calculate C's profit share**:
- Now, substituting x back to find C's share:
\[ C's \, share = 18x = 18 \times 1300 = 23400 \]

Thus, from Statement I, we can determine that C's profit share is Rs. 23,400.

### Step 2: Analyze Statement II
Statement II states that C, D, and F invested in a partnership business in the ratio 54:8:2, with investment periods of 6 months, 4 months, and 12 months respectively. The profit share of F at the end of the year is Rs. 18720.

1. **Calculate the effective investment for each partner**:
- The effective investment can be calculated as:
- C's effective investment = 54 * 6 = 324
- D's effective investment = 8 * 4 = 32
- F's effective investment = 2 * 12 = 24

2. **Find the total effective investment**:
- Total effective investment = 324 + 32 + 24 = 380.

3. **Calculate the profit share ratio**:
- The profit share ratio based on effective investments is:
- C's share = 324
- D's share = 32
- F's share = 24
- The ratio is 324:32:24.

4. **Find the profit share of F**:
- Given that F's profit share is Rs. 18720, we can find the value of one unit:
\[ F's \, share = 24y = 18720 \implies y = \frac{18720}{24} = 780 \]

5. **Calculate C's profit share**:
- Now substituting y back to find C's share:
\[ C's \, share = 324y = 324 \times 780 = 252720 \]

Thus, from Statement II, we can determine that C's profit share is Rs. 252,720.

### Conclusion
Both statements I and II provide sufficient information to determine the profit share of C, but they yield different results. Therefore, we conclude that:

**Either statement I or statement II by itself is sufficient to answer the question.**

### Final Answer
The answer is **Option D: Either statement I or statement II by itself is sufficient to answer the question.**