A company allows `9%` commission on total sales but if the salesman is appointed on a fixed salary of Rs. 4000 and `3%` commission on the sales more than Rs. 10000, then the salesman gets Rs. 700 more. Find the total sales made by the salesman

Answer

To solve the problem, we need to determine the total sales made by the salesman. We will set up equations based on the information provided.

### Step 1: Define the variables
Let the total sales made by the salesman be \( X \) rupees.

### Step 2: Calculate the commission for the first scenario
In the first scenario, the salesman earns a commission of 9% on total sales:
\[ \text{Commission} = \frac{9}{100} \times X = \frac{9X}{100} \]

### Step 3: Calculate the earnings for the second scenario
In the second scenario, the salesman has a fixed salary of Rs. 4000 and earns a 3% commission on sales exceeding Rs. 10,000.

- If \( X \) is greater than Rs. 10,000, the commission on sales exceeding Rs. 10,000 is:
\[ \text{Commission on sales over 10,000} = \frac{3}{100} \times (X - 10000) = \frac{3(X - 10000)}{100} \]
- Therefore, the total earnings in this scenario would be:
\[ \text{Total Earnings} = 4000 + \frac{3(X - 10000)}{100} \]

### Step 4: Simplify the second scenario's earnings
Now, simplify the total earnings:
\[ \text{Total Earnings} = 4000 + \frac{3X - 30000}{100} = 4000 + \frac{3X}{100} - 300 \]
\[ = 4000 - 300 + \frac{3X}{100} = 3700 + \frac{3X}{100} \]

### Step 5: Set up the equation based on the difference in earnings
According to the problem, the second salesman earns Rs. 700 more than the first salesman:
\[ 3700 + \frac{3X}{100} = \frac{9X}{100} + 700 \]

### Step 6: Rearrange the equation
Now, rearranging the equation:
\[ 3700 + \frac{3X}{100} - 700 = \frac{9X}{100} \]
\[ 3000 + \frac{3X}{100} = \frac{9X}{100} \]

### Step 7: Combine like terms
Subtract \(\frac{3X}{100}\) from both sides:
\[ 3000 = \frac{9X}{100} - \frac{3X}{100} \]
\[ 3000 = \frac{6X}{100} \]

### Step 8: Solve for \( X \)
Multiply both sides by 100 to eliminate the fraction:
\[ 3000 \times 100 = 6X \]
\[ 300000 = 6X \]
Now, divide both sides by 6:
\[ X = \frac{300000}{6} = 50000 \]

### Conclusion
The total sales made by the salesman is Rs. 50,000.

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