First trader calculates profit % on CP while second trader calculates his profit % on SP. Both sells their article at same price Rs 3760 and both claims to gain a profit of 17.5% . Find the difference of their actual profit ?

Options

A. Rs 96
B. Rs 90
C. Rs 98
D. Rs 102

Answer

To solve the problem step by step, we will first determine the actual profits of both traders and then find the difference between those profits.

### Step 1: Calculate the Cost Price for the First Trader
The first trader calculates profit percentage on the Cost Price (CP). Given that the Selling Price (SP) is Rs. 3760 and the profit percentage is 17.5%, we can use the formula:

\[ \text{Profit Percentage} = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100 \]

Rearranging the formula to find the Cost Price (CP):

\[ \text{CP} = \frac{\text{SP}}{1 + \frac{\text{Profit Percentage}}{100}} \]

Substituting the values:

\[ \text{CP} = \frac{3760}{1 + \frac{17.5}{100}} = \frac{3760}{1.175} \approx 3200 \]

### Step 2: Calculate the Profit for the First Trader
Now, we can calculate the profit for the first trader:

\[ \text{Profit} = \text{SP} - \text{CP} = 3760 - 3200 = 560 \]

### Step 3: Calculate the Profit for the Second Trader
The second trader calculates profit percentage on the Selling Price (SP). The profit is calculated as:

\[ \text{Profit} = \text{SP} \times \frac{\text{Profit Percentage}}{100} \]

Substituting the values:

\[ \text{Profit} = 3760 \times \frac{17.5}{100} = 3760 \times 0.175 = 658 \]

### Step 4: Find the Difference in Actual Profits
Now, we find the difference between the profits of the two traders:

\[ \text{Difference} = \text{Profit of Second Trader} - \text{Profit of First Trader} = 658 - 560 = 98 \]

### Final Answer
The difference in their actual profits is Rs. 98.

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