Deepak found that he had made a loss of 10% while selling his smartphone. He also found that had he sold it for Rs.50 more, he would have made a profit of 5%. The initial loss was what percentage of the profit earned, had he sold the smartphone for a 5% profit?

Options

A. 1
B. 2
C. 0.75
D. 0.85

Explanation

To solve the problem step by step, let's denote the cost price of the smartphone as \( CP \).

### Step 1: Understand the Loss
Deepak made a loss of 10% while selling the smartphone. This means he sold it for 90% of its cost price.
\[ \text{Selling Price (SP)} = CP - 0.10 \times CP = 0.90 \times CP \]

### Step 2: Understand the Profit
If Deepak had sold the smartphone for Rs. 50 more, he would have made a profit of 5%. This means the new selling price would be:
\[ \text{New SP} = CP + 0.05 \times CP = 1.05 \times CP \]

### Step 3: Set Up the Equation
According to the problem, the new selling price is also equal to the original selling price plus Rs. 50:
\[ 1.05 \times CP = 0.90 \times CP + 50 \]

### Step 4: Solve for Cost Price (CP)
Now, we can solve the equation:
\[ 1.05 \times CP - 0.90 \times CP = 50 \]
\[ 0.15 \times CP = 50 \]
\[ CP = \frac{50}{0.15} = \frac{5000}{15} = 333.33 \]

### Step 5: Calculate Selling Price with 5% Profit
Now that we have the cost price, we can calculate the selling price if he had sold it for a 5% profit:
\[ \text{SP at 5% profit} = 1.05 \times CP = 1.05 \times 333.33 = 350 \]

### Step 6: Calculate the Initial Loss
The initial loss was 10% of the cost price:
\[ \text{Loss} = 0.10 \times CP = 0.10 \times 333.33 = 33.33 \]

### Step 7: Calculate the Profit
The profit earned if he sold it for a 5% profit is:
\[ \text{Profit} = \text{SP at 5% profit} - CP = 350 - 333.33 = 16.67 \]

### Step 8: Find the Percentage of Initial Loss with Respect to Profit
Now, we need to find what percentage the initial loss is of the profit earned:
\[ \text{Percentage} = \left( \frac{\text{Loss}}{\text{Profit}} \right) \times 100 = \left( \frac{33.33}{16.67} \right) \times 100 \approx 200\% \]

### Final Answer
The initial loss was approximately **200%** of the profit earned had he sold the smartphone for a 5% profit.

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