A man wanted to sell an article with 20% profit, but he actually sold at 20% loss for Rs.480 .At what price he wanted to sell it to earn the profit?

Options

A. Rs. 720
B. Rs. 840
C. Rs. 600
D. Rs. 750

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the Problem
The man intended to sell an article at a 20% profit but ended up selling it at a 20% loss for Rs. 480. We need to find out the price he intended to sell it for to achieve the desired profit.

### Step 2: Determine the Selling Price at Loss
The selling price (SP) when sold at a loss is given as Rs. 480.

### Step 3: Calculate the Cost Price (CP)
To find the cost price, we can use the formula for selling price in terms of cost price and loss percentage:
\[ SP = CP \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]
Given that the loss percentage is 20%, we can rewrite the formula as:
\[ 480 = CP \times \left(1 - \frac{20}{100}\right) \]
This simplifies to:
\[ 480 = CP \times 0.8 \]
Now, we can solve for CP:
\[ CP = \frac{480}{0.8} = 600 \]

### Step 4: Calculate the Desired Selling Price for Profit
Now that we have the cost price (CP = Rs. 600), we need to find the selling price (SP) that would yield a 20% profit. The formula for selling price in terms of cost price and profit percentage is:
\[ SP = CP \times \left(1 + \frac{\text{Profit \%}}{100}\right) \]
Substituting the values:
\[ SP = 600 \times \left(1 + \frac{20}{100}\right) \]
This simplifies to:
\[ SP = 600 \times 1.2 \]
Calculating this gives:
\[ SP = 720 \]

### Conclusion
The price at which the man wanted to sell the article to earn a 20% profit is Rs. 720.

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