A,B and C entered into partnership in a business. A got`3//5`of the profit B and C distributed the remaining profit equally. If C got X 400 less than A, the total profit was

Options

A. X 1600
B. X 1200
C. X 1000
D. X 800

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Define the total profit
Let the total profit be denoted as \( x \).

### Step 2: Calculate A's share of the profit
A receives \(\frac{3}{5}\) of the total profit. Therefore, A's share can be calculated as:
\[ \text{A's share} = \frac{3}{5}x \]

### Step 3: Calculate the remaining profit after A's share
The remaining profit after A's share is:
\[ \text{Remaining profit} = x - \frac{3}{5}x \]
To simplify this, we can find a common denominator:
\[ \text{Remaining profit} = \frac{5}{5}x - \frac{3}{5}x = \frac{2}{5}x \]

### Step 4: Distribute the remaining profit between B and C
Since B and C share the remaining profit equally, each of them receives:
\[ \text{B's share} = \text{C's share} = \frac{1}{2} \times \frac{2}{5}x = \frac{1}{5}x \]

### Step 5: Set up the equation based on the information given
According to the problem, C received 400 less than A. Therefore, we can set up the equation:
\[ \text{C's share} = \text{A's share} - 400 \]
Substituting the values we calculated:
\[ \frac{1}{5}x = \frac{3}{5}x - 400 \]

### Step 6: Solve for \( x \)
To solve for \( x \), we first eliminate the fractions by multiplying the entire equation by 5:
\[ x = 3x - 2000 \]
Now, rearranging gives:
\[ 2000 = 3x - x \]
\[ 2000 = 2x \]
Dividing both sides by 2:
\[ x = 1000 \]

### Conclusion
The total profit is \( \text{Rs. } 1000 \).

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