A salesman is allowed `5(1)/(2)%` commision on the total sales made by him plus a bonus of `(1)/(2)%` on sales over Rs. 10,000. If his total earnings were Rs. 1,990, his total sales (in Rs.) was

Options

A. 30000
B. 32000
C. 34000
D. 35000

Answer

To solve the problem step by step, we will first define the variables and then set up the equations based on the information given in the question.

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

### Step 2: Calculate the commission and bonus
The salesman earns a commission of \( 5.5\% \) on his total sales \( X \). This can be expressed as:
\[ \text{Commission} = \frac{5.5}{100} \times X = 0.055X \]

Additionally, he earns a bonus of \( 0.5\% \) on sales over Rs. 10,000. If \( X \) is greater than Rs. 10,000, the bonus can be calculated as:
\[ \text{Bonus} = \frac{0.5}{100} \times (X - 10000) = 0.005(X - 10000) \]

### Step 3: Set up the equation for total earnings
The total earnings of the salesman are given as Rs. 1,990. Therefore, we can set up the following equation:
\[ \text{Total Earnings} = \text{Commission} + \text{Bonus} \]
Substituting the expressions for commission and bonus, we get:
\[ 1990 = 0.055X + 0.005(X - 10000) \]

### Step 4: Simplify the equation
Now, we will simplify the equation:
\[ 1990 = 0.055X + 0.005X - 0.05 \times 10000 \]
Calculating \( 0.05 \times 10000 \):
\[ 0.05 \times 10000 = 500 \]
Thus, the equation becomes:
\[ 1990 = 0.055X + 0.005X - 500 \]
Combining like terms:
\[ 1990 + 500 = 0.055X + 0.005X \]
\[ 2490 = 0.06X \]

### Step 5: Solve for \( X \)
Now, we can solve for \( X \):
\[ X = \frac{2490}{0.06} \]
Calculating \( \frac{2490}{0.06} \):
\[ X = 41500 \]

### Step 6: Conclusion
The total sales made by the salesman is Rs. 41,500.