A company allowed `9%` commission on the total sales made by salesman and a bonus of `1%` on the sales over `Rs. 10,000`. If the salesman deposited `Rs.45100` in the company after deducting his earning from the total sales made by him. Find the total sales ?

Options

A. `50000`
B. `60000`
C. `55000`
D. `65000`

Answer

To solve the problem step by step, we need to determine the total sales made by the salesman based on the commission and bonus structure provided by the company.

### Step 1: Understand the Commission and Bonus Structure
The company provides:
- A commission of 9% on total sales.
- A bonus of 1% on sales exceeding Rs. 10,000.

### Step 2: Define Variables
Let the total sales made by the salesman be \( S \).

### Step 3: Calculate the Earnings
The earnings from the commission and bonus can be calculated as follows:
- The commission earned from total sales \( S \) is \( 0.09S \).
- If \( S \) exceeds Rs. 10,000, the bonus will be \( 1\% \) of the amount over Rs. 10,000. This can be expressed as:
\[ \text{Bonus} = 0.01(S - 10,000) \quad \text{(if } S > 10,000\text{)} \]

### Step 4: Total Earnings
The total earnings of the salesman can be expressed as:
\[ \text{Total Earnings} = 0.09S + 0.01(S - 10,000) \]
This simplifies to:
\[ \text{Total Earnings} = 0.09S + 0.01S - 100 = 0.10S - 100 \]

### Step 5: Calculate the Amount Deposited
According to the problem, the salesman deposited Rs. 45,100 after deducting his earnings from the total sales:
\[ S - \text{Total Earnings} = 45,100 \]
Substituting the expression for Total Earnings:
\[ S - (0.10S - 100) = 45,100 \]
This simplifies to:
\[ S - 0.10S + 100 = 45,100 \]
\[ 0.90S + 100 = 45,100 \]

### Step 6: Solve for \( S \)
Subtract 100 from both sides:
\[ 0.90S = 45,000 \]
Now, divide by 0.90:
\[ S = \frac{45,000}{0.90} = 50,000 \]

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

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