A salesman is allowed `5.5 %` commission on the sales made by him up to Rs. 10000 and additional bonus of 0.5 % on sale over Rs 10000. If his total earnings are Rs. 1990. Find the total sales made by him?

Answer

To solve the problem step by step, we will break down the calculations based on the information provided.

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

### Step 2: Calculate the commission for sales up to Rs. 10,000
The salesman earns a commission of \( 5.5\% \) on sales up to Rs. 10,000. Therefore, the commission for the first Rs. 10,000 is:
\[ \text{Commission} = 5.5\% \text{ of } 10,000 = \frac{5.5}{100} \times 10,000 = 550 \text{ Rs.} \]

### Step 3: Calculate the sales over Rs. 10,000
If the total sales \( X \) is greater than Rs. 10,000, then the sales over Rs. 10,000 can be calculated as:
\[ \text{Sales over } 10,000 = X - 10,000 \]

### Step 4: Calculate the bonus for sales over Rs. 10,000
The salesman earns an additional bonus of \( 0.5\% \) on the sales amount over Rs. 10,000. Therefore, the bonus is:
\[ \text{Bonus} = 0.5\% \text{ of } (X - 10,000) = \frac{0.5}{100} \times (X - 10,000) = 0.005 \times (X - 10,000) \]

### Step 5: Write the equation for total earnings
The total earnings of the salesman is the sum of the commission and the bonus. According to the problem, his total earnings are Rs. 1990. Thus, we can write the equation:
\[ 550 + 0.005 \times (X - 10,000) = 1990 \]

### Step 6: Simplify the equation
First, isolate the bonus term:
\[ 0.005 \times (X - 10,000) = 1990 - 550 \]
\[ 0.005 \times (X - 10,000) = 1440 \]

### Step 7: Solve for \( X \)
Now, divide both sides by \( 0.005 \):
\[ X - 10,000 = \frac{1440}{0.005} \]
\[ X - 10,000 = 288,000 \]
Now, add 10,000 to both sides:
\[ X = 288,000 + 10,000 \]
\[ X = 298,000 \]

### Step 8: Final answer
Thus, the total sales made by the salesman is:
\[ \text{Total Sales} = Rs. 298,000 \]