A,B & C enters into a partnership with a total capital of Rs .11800 .A's Capital is Rs. 2000 more than B's & Rs. 3000 less than C. At the end of the year , what is B's share in the profit if total profit is Rs. 35400.

Options

A. Rs . 14800
B. Rs . 6600
C. Rs . 10800
D. Rs .4800

Answer

To solve the problem step by step, we will first define the capital contributions of A, B, and C based on the information given in the question.

### Step 1: Define the variables
Let:
- B's capital = Rs. x
- A's capital = Rs. (x + 2000) (since A's capital is Rs. 2000 more than B's)
- C's capital = Rs. (x + 2000 + 3000) = Rs. (x + 5000) (since A's capital is Rs. 3000 less than C's)

### Step 2: Set up the equation for total capital
According to the problem, the total capital of A, B, and C is Rs. 11800. Therefore, we can write the equation:
\[ A + B + C = 11800 \]
Substituting the expressions for A and C:
\[ (x + 2000) + x + (x + 5000) = 11800 \]

### Step 3: Simplify the equation
Combine like terms:
\[ 3x + 7000 = 11800 \]

### Step 4: Solve for x
Subtract 7000 from both sides:
\[ 3x = 11800 - 7000 \]
\[ 3x = 4800 \]
Now, divide by 3:
\[ x = \frac{4800}{3} = 1600 \]

### Step 5: Calculate the capital contributions
Now that we have B's capital (x), we can find A's and C's capitals:
- B's capital = Rs. 1600
- A's capital = Rs. (1600 + 2000) = Rs. 3600
- C's capital = Rs. (1600 + 5000) = Rs. 6600

### Step 6: Determine the profit-sharing ratio
The ratio of their capitals is:
- A : B : C = 3600 : 1600 : 6600

To simplify this ratio, we can divide each term by 200:
- A : B : C = 18 : 8 : 33

### Step 7: Calculate the total parts in the ratio
Total parts = 18 + 8 + 33 = 59 parts

### Step 8: Calculate the value of one part
The total profit is Rs. 35400. Therefore, the value of one part is:
\[ \text{Value of one part} = \frac{35400}{59} = 600 \]

### Step 9: Calculate B's share of the profit
B's share in the profit corresponds to 8 parts:
\[ \text{B's profit} = 8 \times 600 = 4800 \]

### Final Answer
B's share in the profit is Rs. 4800.

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