A salesman is appointed on the basic salary of `Rs.1200` per month and the condition that for every sales of `Rs.10000` and above `Rs10000` he will get `50%` of basic salary and `10%` of the sales as reward this incentive scheme does not operate for the first `Rs.10,000` of sales. What shoul be the value of sales, if he wants to earn `Rs. 7600` in a particular month ?

Options

A. `48000`
B. `45500`
C. `50000`
D. `49000`

Answer

To solve the problem step-by-step, let's break it down:

### Step 1: Understand the Salary Structure
The salesman has a basic salary of Rs. 1200 per month. For sales above Rs. 10,000, he receives:
- 50% of his basic salary as a fixed incentive.
- 10% of the sales amount above Rs. 10,000 as a variable incentive.

### Step 2: Calculate the Fixed Incentive
The fixed incentive he receives for sales above Rs. 10,000 is:
\[ \text{Fixed Incentive} = 50\% \text{ of Basic Salary} = 0.5 \times 1200 = Rs. 600 \]

### Step 3: Determine the Total Earnings Desired
The total earnings he wants to achieve in a month is Rs. 7600.

### Step 4: Calculate the Variable Incentive Needed
To find out how much variable incentive he needs, we subtract the fixed incentive from the total desired earnings:
\[ \text{Variable Incentive Needed} = \text{Total Earnings} - \text{Fixed Incentive} \]
\[ \text{Variable Incentive Needed} = 7600 - 600 = Rs. 7000 \]

### Step 5: Set Up the Equation for Sales
The variable incentive is calculated as 10% of the sales amount above Rs. 10,000. Let \( S \) be the total sales amount. The sales amount above Rs. 10,000 is \( S - 10000 \). Therefore, we can express the variable incentive as:
\[ \text{Variable Incentive} = 10\% \text{ of } (S - 10000) = 0.1 \times (S - 10000) \]
Setting this equal to the variable incentive needed:
\[ 0.1 \times (S - 10000) = 7000 \]

### Step 6: Solve for \( S \)
To solve for \( S \), first multiply both sides by 10 to eliminate the decimal:
\[ S - 10000 = 70000 \]
Now, add 10000 to both sides:
\[ S = 70000 + 10000 = 80000 \]

### Step 7: Conclusion
The total sales amount required for the salesman to earn Rs. 7600 in a month is:
\[ \boxed{80000} \]

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