A working partner gets 20% as his commission of the profit after his commission is paid. If the working partner's commission is Rs. 800, then what is the total profit in the business?

Answer

To solve the problem step by step, we need to determine the total profit in the business based on the working partner's commission.

### Step 1: Understand the commission structure
The working partner receives 20% of the profit after his commission is paid. This means if we denote the total profit as \( P \), then the commission can be expressed as:
\[ \text{Commission} = 20\% \text{ of } (P - \text{Commission}) \]

### Step 2: Set up the equation
Let the commission be \( C \). According to the problem, we know that:
\[ C = 0.2 \times (P - C) \]
Given that the commission \( C \) is Rs. 800, we can substitute:
\[ 800 = 0.2 \times (P - 800) \]

### Step 3: Solve for \( P \)
Now, we can solve the equation for \( P \):
1. Multiply both sides by 5 to eliminate the decimal:
\[ 4000 = P - 800 \]
2. Add 800 to both sides:
\[ P = 4000 + 800 \]
\[ P = 4800 \]

### Step 4: Conclusion
The total profit in the business is Rs. 4800.

### Summary of Steps:
1. Understand the commission structure.
2. Set up the equation based on the given commission.
3. Solve the equation for total profit \( P \).
4. Conclude with the total profit amount.

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