A, B and C entered into a partnership. IF the profit earned in the business is proportional to the investment and the period of investment then What is the profit of B if all of them invested the amount for one year and total profit is Rs.x.
A. A invested Rs.1500 more than that of C.
B. A invested 2 times more than that of B. C invested 3 times more than that of A.
C. B invested 200 percent more than that of A and `100%` less than that of C. (a) Any two of them (b) B or C alone (c) Any of them (d) None of these

Options

A. Any two of them
B. Either B or C alone
C. Any of them
D. None of these

Explanation

To solve the problem, we need to analyze the information provided in the statements about the investments made by A, B, and C, and how these investments relate to the profits they earn.

### Step 1: Analyze Statement A
Statement A says that A invested Rs. 1500 more than C.
- Let C's investment be \( C \).
- Then A's investment can be expressed as \( A = C + 1500 \).

### Step 2: Analyze Statement B
Statement B states that A invested 2 times more than B, and C invested 3 times more than A.
- If we let B's investment be \( B \), then A's investment can be expressed as \( A = 2B \).
- Since C invested 3 times more than A, we can express C's investment as \( C = 3A = 3(2B) = 6B \).

### Step 3: Combine Statements A and B
From Statement A, we have:
1. \( A = C + 1500 \)
2. From Statement B, we have \( A = 2B \) and \( C = 6B \).

Substituting \( C \) from Statement B into Statement A:
\[ A = 6B + 1500 \]
Now, equate the two expressions for A:
\[ 2B = 6B + 1500 \]
Rearranging gives:
\[ 2B - 6B = 1500 \implies -4B = 1500 \implies B = -375 \]
This indicates a contradiction since investments cannot be negative. Therefore, we need to check the statements independently.

### Step 4: Analyze Statement C
Statement C states that B invested 200% more than A and 100% less than C.
- If A's investment is \( A \), then B's investment can be expressed as:
\[ B = A + 2A = 3A \]
- If B invested 100% less than C, then C's investment can be expressed as:
\[ C = B + B = 2B = 2(3A) = 6A \]

### Step 5: Calculate Total Investments
Now we have:
- From Statement B: \( A = 2B \) and \( C = 6B \)
- From Statement C: \( B = 3A \) and \( C = 6A \)

### Step 6: Calculate Profit of B
The total investment can be expressed as:
\[ Total = A + B + C = 2B + B + 6B = 9B \]
The profit of B is proportional to his investment:
\[ Profit_B = \frac{B}{Total} \times X = \frac{B}{9B} \times X = \frac{1}{9}X \]

### Conclusion
To find the profit of B, we can use either Statement B or Statement C alone, as both provide sufficient information to calculate B's profit based on the total profit \( X \).

### Final Answer
The answer is (b) B or C alone.