A, B and C subscribe Rs. 47000 for a business . A subscribes Rs. 7000 more than B and B Rs. 5000 more than C. Out of a total profit of Rs. 9400 , B receives

Options

A. Rs 4400
B. Rs 3000
C. RS 2000
D. Rs 1737.90

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Define the Investments
Let the investment of C be Rs. X.
- Then, the investment of B will be Rs. (X + 5000).
- The investment of A will be Rs. (X + 5000 + 7000) = Rs. (X + 12000).

### Step 2: Set Up the Equation
According to the problem, the total investment of A, B, and C is Rs. 47000. Therefore, we can set up the equation:
\[ A + B + C = 47000 \]
Substituting the expressions for A, B, and C:
\[ (X + 12000) + (X + 5000) + X = 47000 \]

### Step 3: Simplify the Equation
Combine like terms:
\[ 3X + 17000 = 47000 \]

### Step 4: Solve for X
Subtract 17000 from both sides:
\[ 3X = 47000 - 17000 \]
\[ 3X = 30000 \]
Now, divide by 3:
\[ X = 10000 \]

### Step 5: Calculate Individual Investments
Now that we have X, we can find the investments of A, B, and C:
- Investment of C (C_i) = Rs. X = Rs. 10000
- Investment of B (B_i) = Rs. (X + 5000) = Rs. (10000 + 5000) = Rs. 15000
- Investment of A (A_i) = Rs. (X + 12000) = Rs. (10000 + 12000) = Rs. 22000

### Step 6: Find the Ratio of Investments
The ratio of investments A:B:C is:
\[ A_i : B_i : C_i = 22000 : 15000 : 10000 \]
To simplify, we can divide each term by 1000:
\[ 22 : 15 : 10 \]

### Step 7: Calculate B's Share of the Profit
The total profit is Rs. 9400. The share of B from the profit can be calculated using the ratio of investments:
\[ \text{B's share} = \left( \frac{B_i}{A_i + B_i + C_i} \right) \times \text{Total Profit \]
Substituting the values:
\[ \text{B's share} = \left( \frac{15000}{22000 + 15000 + 10000} \right) \times 9400 \]
\[ = \left( \frac{15000}{47000} \right) \times 9400 \]

### Step 8: Simplify and Calculate
Calculating the fraction:
\[ = \left( \frac{15}{47} \right) \times 9400 \]
Now, calculate:
\[ = 15 \times 200 = 3000 \]

### Final Answer
B receives Rs. 3000 from the total profit.

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