A shoe salesman gets `10%` commision on the total sales and on extra bonus of `2.5%` on the sales above `Rs.10000`. If he earns `Rs.2875`. Find the total sales.

Options

A. `30000`
B. `35000`
C. `25000`
D. `32000`

Answer

To solve the problem, we need to find the total sales made by the shoe salesman based on his earnings from commissions and bonuses.

Let's denote the total sales as \( S \).

### Step 1: Understand the commission structure
The salesman earns a commission of:
- 10% on the total sales \( S \)
- An additional 2.5% on the amount exceeding Rs. 10,000

### Step 2: Calculate the commission for sales above Rs. 10,000
If the total sales \( S \) is greater than Rs. 10,000, the commission can be broken down into two parts:
1. For the first Rs. 10,000, he earns:
\[ \text{Commission on } 10,000 = 10\% \times 10,000 = 0.1 \times 10,000 = 1,000 \]
2. For the amount exceeding Rs. 10,000, say \( S - 10,000 \), he earns:
\[ \text{Commission on } (S - 10,000) = 12.5\% \times (S - 10,000) = 0.125 \times (S - 10,000) \]

### Step 3: Set up the equation for total earnings
The total earnings from commissions can be expressed as:
\[ \text{Total Earnings} = \text{Commission on } 10,000 + \text{Commission on } (S - 10,000) \]
Thus, we have:
\[ 2875 = 1000 + 0.125 \times (S - 10,000) \]

### Step 4: Simplify the equation
Subtract 1000 from both sides:
\[ 2875 - 1000 = 0.125 \times (S - 10,000) \]
\[ 1875 = 0.125 \times (S - 10,000) \]

### Step 5: Solve for \( S - 10,000 \)
To isolate \( S - 10,000 \), divide both sides by 0.125:
\[ S - 10,000 = \frac{1875}{0.125} \]
Calculating the right side:
\[ S - 10,000 = 1875 \div 0.125 = 15000 \]

### Step 6: Solve for total sales \( S \)
Now, add 10,000 to both sides to find \( S \):
\[ S = 15000 + 10000 = 25000 \]

### Conclusion
The total sales made by the shoe salesman is \( \text{Rs. } 25000 \).

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