Arvind purchased a wrist watch with 30% discount on the labelled price. He sold it with 40% profit on the price he bought. What was his percent loss on the labelled price?

Options

A. 0.02
B. 0.06
C. 0.04
D. 0.08

Answer

To solve the problem step by step, let's define the variables and calculate the required values.

### Step 1: Define the Label Price
Let the label price (marked price) of the wrist watch be \( P \).

### Step 2: Calculate the Cost Price
Arvind purchased the wrist watch with a 30% discount on the label price. Therefore, the cost price (CP) can be calculated as follows:

\[ \text{Discount} = 30\% \text{ of } P = 0.30P \]
\[ \text{Cost Price (CP)} = P - \text{Discount} = P - 0.30P = 0.70P \]

### Step 3: Calculate the Selling Price
Arvind sold the wrist watch at a 40% profit on the cost price. The selling price (SP) can be calculated as follows:

\[ \text{Profit} = 40\% \text{ of CP} = 0.40 \times 0.70P = 0.28P \]
\[ \text{Selling Price (SP)} = CP + \text{Profit} = 0.70P + 0.28P = 0.98P \]

### Step 4: Calculate the Loss on the Label Price
Now, we need to find the percent loss on the label price. The loss can be calculated as follows:

\[ \text{Loss} = \text{Label Price} - \text{Selling Price} = P - 0.98P = 0.02P \]

### Step 5: Calculate the Percent Loss
To find the percent loss on the label price, we use the formula:

\[ \text{Percent Loss} = \left( \frac{\text{Loss}}{\text{Label Price}} \right) \times 100 \]
Substituting the values we have:

\[ \text{Percent Loss} = \left( \frac{0.02P}{P} \right) \times 100 = 2\% \]

### Final Answer
Arvind's percent loss on the labelled price is **2%**.

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