A salesman expects a gain of 13% on his cost price. If in a month, his sale was X 791000, what was his profit?

Options

A. X 91000
B. X 97786
C. X 85659
D. X 88300

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Understand the relationship between Selling Price (SP), Cost Price (CP), and Profit.
The profit percentage is given as 13%. This means that the Selling Price (SP) is 13% more than the Cost Price (CP).

### Step 2: Write the formula for Selling Price in terms of Cost Price.
The relationship can be expressed as:
\[ SP = CP + (13\% \text{ of } CP) \]
This can be rewritten as:
\[ SP = CP \times (1 + 0.13) \]
or
\[ SP = CP \times 1.13 \]

### Step 3: Rearrange the formula to find Cost Price.
To find the Cost Price (CP), we can rearrange the formula:
\[ CP = \frac{SP}{1.13} \]

### Step 4: Substitute the Selling Price into the formula.
Given that the Selling Price (SP) is ₹791,000, we can substitute this value into the formula:
\[ CP = \frac{791000}{1.13} \]

### Step 5: Calculate the Cost Price.
Now, we will perform the calculation:
\[ CP = \frac{791000}{1.13} \approx 700000 \]

### Step 6: Calculate the Profit.
Now that we have the Cost Price, we can calculate the Profit. The Profit is 13% of the Cost Price:
\[ \text{Profit} = 13\% \text{ of } CP \]
\[ \text{Profit} = 0.13 \times 700000 \]
\[ \text{Profit} = 91000 \]

### Final Answer:
The profit made by the salesman is ₹91,000.

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