A salesman in allowed `8%` commission on the total sales made by him and a bonus of `2%` on the sales over `Rs.20,000`. If the total earning of a salesman is `Rs. 7600`. Find the total sale ?

Options

A. `78000`
B. `70000`
C. `80000`
D. `90500`

Answer

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

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

### Step 2: Calculate the commission
The salesman earns an 8% commission on the total sales. Therefore, the commission can be calculated as:
\[ \text{Commission} = \frac{8}{100} \times X = 0.08X \]

### Step 3: Calculate the bonus
The salesman also earns a bonus of 2% on the sales over Rs. 20,000. This means that if the total sales \( X \) is greater than Rs. 20,000, the bonus will be:
\[ \text{Bonus} = \frac{2}{100} \times (X - 20000) = 0.02(X - 20000) \]
This bonus is applicable only if \( X > 20000 \).

### Step 4: Set up the total earnings equation
The total earnings of the salesman is given as Rs. 7600. Therefore, we can write the equation for total earnings as:
\[ \text{Total Earnings} = \text{Commission} + \text{Bonus} \]
Substituting the values we have:
\[ 7600 = 0.08X + 0.02(X - 20000) \]

### Step 5: Simplify the equation
Now, we will simplify the equation:
\[ 7600 = 0.08X + 0.02X - 0.02 \times 20000 \]
Calculating \( 0.02 \times 20000 \):
\[ 0.02 \times 20000 = 400 \]
So the equation becomes:
\[ 7600 = 0.08X + 0.02X - 400 \]
Combining like terms:
\[ 7600 + 400 = 0.08X + 0.02X \]
\[ 8000 = 0.10X \]

### Step 6: Solve for \( X \)
Now, we can solve for \( X \):
\[ X = \frac{8000}{0.10} = 80000 \]

### Conclusion
The total sales made by the salesman is Rs. 80,000.