A salesman is allowed `7.5 %` commission on the sale made by him up to Rs. 12000 and additional bonus of `1.5 %` on sale made over Rs 12000. If his total earning is Rs. 4185. Find the total sales made by him?

Answer

To find the total sales made by the salesman, we can follow these steps:

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

### Step 2: Calculate commission for sales up to Rs. 12,000
The salesman earns a commission of \( 7.5\% \) on sales up to Rs. 12,000. Therefore, the commission earned on Rs. 12,000 is:
\[ \text{Commission on Rs. 12,000} = 7.5\% \text{ of } 12,000 = \frac{7.5}{100} \times 12,000 = 900 \text{ Rs.} \]

### Step 3: Calculate sales over Rs. 12,000
If the total sales \( X \) is greater than Rs. 12,000, the amount over Rs. 12,000 is:
\[ \text{Sales over Rs. 12,000} = X - 12,000 \]

### Step 4: Calculate bonus for sales over Rs. 12,000
The salesman earns an additional bonus of \( 1.5\% \) on the sales made over Rs. 12,000. Therefore, the bonus earned on the sales over Rs. 12,000 is:
\[ \text{Bonus} = 1.5\% \text{ of } (X - 12,000) = \frac{1.5}{100} \times (X - 12,000) = \frac{1.5(X - 12,000)}{100} \]

### Step 5: Write the equation for total earnings
The total earnings of the salesman is given as Rs. 4,185. Therefore, we can write the equation:
\[ \text{Total Earnings} = \text{Commission} + \text{Bonus} \]
Substituting the values we calculated:
\[ 4,185 = 900 + \frac{1.5(X - 12,000)}{100} \]

### Step 6: Simplify the equation
Subtract 900 from both sides:
\[ 4,185 - 900 = \frac{1.5(X - 12,000)}{100} \]
\[ 3,285 = \frac{1.5(X - 12,000)}{100} \]

### Step 7: Multiply both sides by 100 to eliminate the fraction
\[ 3,285 \times 100 = 1.5(X - 12,000) \]
\[ 328,500 = 1.5(X - 12,000) \]

### Step 8: Divide both sides by 1.5
\[ \frac{328,500}{1.5} = X - 12,000 \]
Calculating the left side:
\[ 219,000 = X - 12,000 \]

### Step 9: Solve for \( X \)
Add 12,000 to both sides:
\[ X = 219,000 + 12,000 \]
\[ X = 231,000 \]

### Conclusion
The total sales made by the salesman is Rs. 231,000.

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