A salesman is allowed `9.25 %` commission on the sale made by him up to Rs. 20000 and additional bonus of `0.75 %` on sale made over Rs. 20000. If his total earning is Rs. 6170. Find the total sales made by him?

Answer

To find the total sales made by the salesman, we can break down the problem step by step.

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

### Step 2: Determine the commission and bonus structure
- The salesman earns a commission of \( 9.25\% \) on the first \( Rs. 20,000 \).
- If the total sales exceed \( Rs. 20,000 \), he earns an additional \( 0.75\% \) on the amount over \( Rs. 20,000 \).

### Step 3: Calculate the commission for sales up to Rs. 20,000
If \( x \leq 20,000 \):
- The total earnings from commission would be:
\[ \text{Earnings} = 9.25\% \text{ of } x = \frac{9.25}{100} \times x \]

If \( x > 20,000 \):
- The earnings from the first \( Rs. 20,000 \) would be:
\[ \text{Earnings from } 20,000 = 9.25\% \text{ of } 20,000 = \frac{9.25}{100} \times 20,000 = 1850 \]
- The earnings from the amount over \( Rs. 20,000 \) would be:
\[ \text{Earnings from excess} = 0.75\% \text{ of } (x - 20,000) = \frac{0.75}{100} \times (x - 20,000) \]

### Step 4: Set up the equation for total earnings
Given that the total earnings are \( Rs. 6170 \), we can set up the equation based on whether \( x \) is greater than or less than \( Rs. 20,000 \).

If \( x > 20,000 \):
\[ 1850 + \frac{0.75}{100} \times (x - 20,000) = 6170 \]

### Step 5: Solve for \( x \)
1. Subtract \( 1850 \) from both sides:
\[ \frac{0.75}{100} \times (x - 20,000) = 6170 - 1850 \]
\[ \frac{0.75}{100} \times (x - 20,000) = 4320 \]

2. Multiply both sides by \( \frac{100}{0.75} \):
\[ x - 20,000 = 4320 \times \frac{100}{0.75} \]
\[ x - 20,000 = 576000 \]

3. Add \( 20,000 \) to both sides:
\[ x = 576000 + 20,000 \]
\[ x = 596000 \]

### Final Answer
The total sales made by the salesman is \( Rs. 596000 \).

---