A salesman is hired on the condition a job saying that he will be given `6%` commission on the sales done by him. But lates on it was decided that he will be given a monthly salary of `Rs.1200` and every month , `3%` commisssion will be awarded on sales above `Rs.5000`. If in second case his earnings are `1350` less than earlier, then find his sales per month.

Options

A. `90000`
B. `70500`
C. `80000`
D. `75000`

Answer

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

### Step 1: Determine the earnings in the first case
In the first case, the salesman earns a commission of 6% on his total sales.

Let the total sales be \( X \).

The earnings from commission in the first case would be:
\[ \text{Earnings}_1 = 0.06X \]

### Step 2: Determine the earnings in the second case
In the second case, the salesman earns a fixed salary of Rs. 1200 and a commission of 3% on sales above Rs. 5000.

If his total sales \( X \) is greater than Rs. 5000, then the commission on sales above Rs. 5000 can be calculated as follows:

\[ \text{Commission on sales above 5000} = 0.03(X - 5000) \]

Thus, the total earnings in the second case would be:
\[ \text{Earnings}_2 = 1200 + 0.03(X - 5000) \]

### Step 3: Set up the equation based on the difference in earnings
According to the problem, the earnings in the second case are Rs. 1350 less than in the first case. Therefore, we can set up the equation:
\[ \text{Earnings}_2 = \text{Earnings}_1 - 1350 \]

Substituting the expressions we derived:
\[ 1200 + 0.03(X - 5000) = 0.06X - 1350 \]

### Step 4: Simplify the equation
Let's simplify the equation step by step:

1. Expand the left side:
\[ 1200 + 0.03X - 150 = 0.06X - 1350 \]
This simplifies to:
\[ 1050 + 0.03X = 0.06X - 1350 \]

2. Rearranging the equation gives:
\[ 1050 + 1350 = 0.06X - 0.03X \]
Which simplifies to:
\[ 2400 = 0.03X \]

### Step 5: Solve for \( X \)
To find \( X \), divide both sides by 0.03:
\[ X = \frac{2400}{0.03} = 80000 \]

### Conclusion
Thus, the total sales per month of the salesman is Rs. 80000.

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