A company give `14%` commission to his salesman on total sales and `6%` bonus on the sales over `Rs.25000`. If the salesman deposit `Rs.57500` after deducting his earning from total sales. Find total sales.

Options

A. `55000`
B. `70000`
C. `75000`
D. `65000`

Answer

To solve the problem step by step, we will break down the commission and bonus structure and then find the total sales based on the amount deposited by the salesman.

### Step 1: Understand the commission and bonus structure
The salesman receives:
- **14% commission** on total sales.
- **6% bonus** on sales exceeding Rs. 25,000.

### Step 2: Let the total sales be \( x \)
We need to express the earnings of the salesman in terms of \( x \).

### Step 3: Calculate the commission on total sales
The commission on total sales is:
\[ \text{Commission} = 14\% \text{ of } x = 0.14x \]

### Step 4: Calculate the bonus on sales over Rs. 25,000
If \( x \) exceeds Rs. 25,000, the bonus is calculated on the amount over Rs. 25,000:
\[ \text{Bonus} = 6\% \text{ of } (x - 25000) = 0.06(x - 25000) \]

### Step 5: Total earnings of the salesman
The total earnings of the salesman can be expressed as:
\[ \text{Total Earnings} = \text{Commission} + \text{Bonus} \]
Substituting the values we found:
\[ \text{Total Earnings} = 0.14x + 0.06(x - 25000) \]

### Step 6: Simplify the total earnings expression
Expanding the bonus term:
\[ \text{Total Earnings} = 0.14x + 0.06x - 0.06 \times 25000 \]
\[ \text{Total Earnings} = 0.14x + 0.06x - 1500 \]
\[ \text{Total Earnings} = 0.20x - 1500 \]

### Step 7: Relate total earnings to the amount deposited
According to the problem, the salesman deposited Rs. 57,500 after deducting his earnings from total sales. Thus:
\[ x - \text{Total Earnings} = 57500 \]
Substituting the expression for Total Earnings:
\[ x - (0.20x - 1500) = 57500 \]

### Step 8: Solve for \( x \)
Rearranging the equation:
\[ x - 0.20x + 1500 = 57500 \]
\[ 0.80x + 1500 = 57500 \]
Subtracting 1500 from both sides:
\[ 0.80x = 57500 - 1500 \]
\[ 0.80x = 56000 \]
Now, divide both sides by 0.80:
\[ x = \frac{56000}{0.80} \]
\[ x = 70000 \]

### Final Answer
The total sales made by the salesman is **Rs. 70,000**.

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