A trader sold an article at a loss of `5%` but when he increased the selling price by ₹ 65 he gained `3.33%` on the cost price. If he sells the same article at ₹ 936, what is the profit percentage?

Options

A. `15%`
B. `16.66%`
C. `20%`
D. data insufficient

Answer

To solve the problem step by step, let's break down the information given and perform the necessary calculations.

### Step 1: Define the Cost Price (CP)
Let the cost price of the article be \( CP = 300x \).

### Step 2: Calculate the Selling Price (SP) at 5% Loss
Since the trader sells the article at a loss of 5%, we can calculate the selling price as follows:
- Loss = 5% of \( CP = 0.05 \times 300x = 15x \)
- Therefore, the selling price at a loss is:
\[ SP = CP - \text{Loss} = 300x - 15x = 285x \]

### Step 3: Calculate the Selling Price (SP) at 3.33% Gain
When the selling price is increased by ₹65, the trader gains 3.33% on the cost price. We can express 3.33% as a fraction:
- \( 3.33\% = \frac{10}{3} \% = \frac{1}{30} \)
- Thus, the selling price at a gain of 3.33% is:
\[ SP = CP + \text{Gain} = CP \times \left(1 + \frac{10}{300}\right) = 300x \times \frac{310}{300} = 310x \]

### Step 4: Set Up the Equation
According to the problem, the difference between the two selling prices is ₹65:
\[ 310x - 285x = 65 \]
This simplifies to:
\[ 25x = 65 \]

### Step 5: Solve for x
Now, we can solve for \( x \):
\[ x = \frac{65}{25} = 2.6 \]

### Step 6: Calculate the Cost Price (CP)
Now we can find the cost price:
\[ CP = 300x = 300 \times 2.6 = 780 \]

### Step 7: Calculate the Selling Price (SP) when sold at ₹936
The selling price when the article is sold at ₹936 is given as:
\[ SP = 936 \]

### Step 8: Calculate the Profit
Now, we can calculate the profit:
\[ \text{Profit} = SP - CP = 936 - 780 = 156 \]

### Step 9: Calculate the Profit Percentage
Finally, we can calculate the profit percentage:
\[ \text{Profit Percentage} = \left(\frac{\text{Profit}}{CP}\right) \times 100 = \left(\frac{156}{780}\right) \times 100 \]
Calculating this gives:
\[ \text{Profit Percentage} = 20\% \]

### Final Answer
The profit percentage when the article is sold at ₹936 is **20%**.

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