A salesman is allowed `12 %` commission on the sale by him up to Rs. 15000 and additional bonus of `1%` on sale made over Rs 15000. If his total earnings are Rs. 7650. 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 the commission on the first Rs. 15,000
The salesman earns a commission of \( 12\% \) on sales up to Rs. 15,000. Therefore, the commission on Rs. 15,000 is:
\[ \text{Commission on Rs. 15,000} = 12\% \text{ of } 15,000 = \frac{12}{100} \times 15,000 = 1,800 \]

### Step 3: Calculate the sales amount over Rs. 15,000
If the total sales \( x \) is more than Rs. 15,000, the amount over Rs. 15,000 is:
\[ \text{Sales over Rs. 15,000} = x - 15,000 \]

### Step 4: Calculate the bonus on the sales over Rs. 15,000
The salesman earns an additional bonus of \( 1\% \) on the sales made over Rs. 15,000. Therefore, the bonus is:
\[ \text{Bonus} = 1\% \text{ of } (x - 15,000) = \frac{1}{100} \times (x - 15,000) \]

### Step 5: Set up the equation for total earnings
The total earnings of the salesman is the sum of the commission and the bonus:
\[ \text{Total Earnings} = \text{Commission} + \text{Bonus} \]
Given that the total earnings are Rs. 7,650, we can write:
\[ 7,650 = 1,800 + \frac{1}{100} \times (x - 15,000) \]

### Step 6: Simplify the equation
Subtract the commission from both sides:
\[ 7,650 - 1,800 = \frac{1}{100} \times (x - 15,000) \]
\[ 5,850 = \frac{1}{100} \times (x - 15,000) \]

### Step 7: Multiply both sides by 100
To eliminate the fraction, multiply both sides by 100:
\[ 5,850 \times 100 = x - 15,000 \]
\[ 585,000 = x - 15,000 \]

### Step 8: Solve for \( x \)
Add 15,000 to both sides:
\[ x = 585,000 + 15,000 \]
\[ x = 600,000 \]

### Conclusion
The total sales made by the salesman is Rs. 600,000.

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