A merchant purchases a wrist watch for Rs1200 and fixes its list price in sucha way that after allowing a discount of 10%, he earns a profit of 20%.The list price of the watch is.

Options

A. Rs 1,800
B. Rs 1,200
C. Rs 1,600
D. Rs 1,400

Answer

To solve the problem, we need to find the list price of the wristwatch based on the given conditions. Let's break it down step by step.

### Step 1: Determine the Cost Price (CP) and Profit Percentage
The cost price (CP) of the wristwatch is given as Rs. 1200. The merchant wants to earn a profit of 20%.

**Formula for Profit:**
\[ \text{Profit} = \text{CP} \times \frac{\text{Profit Percentage}}{100} \]

**Calculation:**
\[ \text{Profit} = 1200 \times \frac{20}{100} = 1200 \times 0.2 = 240 \]

### Step 2: Calculate the Selling Price (SP)
The selling price (SP) can be calculated by adding the profit to the cost price.

**Formula:**
\[ \text{SP} = \text{CP} + \text{Profit} \]

**Calculation:**
\[ \text{SP} = 1200 + 240 = 1440 \]

### Step 3: Determine the List Price (LP) Considering the Discount
The merchant allows a discount of 10% on the list price (LP). The selling price (SP) is related to the list price (LP) by the formula:

**Formula:**
\[ \text{SP} = \text{LP} - \left( \text{LP} \times \frac{\text{Discount Percentage}}{100} \right) \]
or
\[ \text{SP} = \text{LP} \times \left(1 - \frac{\text{Discount Percentage}}{100}\right) \]

**Calculation:**
Substituting the values we have:
\[ 1440 = \text{LP} \times \left(1 - \frac{10}{100}\right) \]
\[ 1440 = \text{LP} \times 0.9 \]

### Step 4: Solve for the List Price (LP)
To find the list price, we rearrange the equation:

**Formula:**
\[ \text{LP} = \frac{1440}{0.9} \]

**Calculation:**
\[ \text{LP} = 1600 \]

### Conclusion
The list price of the wristwatch is Rs. 1600.

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