By selling an article for Rs. 320, a man incurs a loss of 20%. What should be the selling price of an article to gain 20% ?

Options

A. Rs. 450
B. Rs. 480
C. Rs. 420
D. Rs. 500

Answer

To solve the problem step by step, we need to find the cost price (CP) of the article first and then determine the selling price (SP) for a 20% gain.

### Step 1: Understand the given information
We know that:
- Selling Price (SP) = Rs. 320
- Loss Percentage = 20%

### Step 2: Calculate the Cost Price (CP)
When there is a loss of 20%, it means the selling price is 80% of the cost price. We can express this mathematically as:
\[ SP = CP \times \left(1 - \frac{Loss\%}{100}\right) \]
Substituting the known values:
\[ 320 = CP \times \left(1 - \frac{20}{100}\right) \]
This simplifies to:
\[ 320 = CP \times 0.8 \]
To find CP, we divide both sides by 0.8:
\[ CP = \frac{320}{0.8} \]
Calculating this gives:
\[ CP = 400 \]

### Step 3: Calculate the Selling Price for a 20% Gain
Now that we have the cost price, we can find the selling price for a 20% gain. The selling price for a gain can be calculated using the formula:
\[ SP = CP \times \left(1 + \frac{Gain\%}{100}\right) \]
Substituting the values:
\[ SP = 400 \times \left(1 + \frac{20}{100}\right) \]
This simplifies to:
\[ SP = 400 \times 1.2 \]
Calculating this gives:
\[ SP = 480 \]

### Final Answer
The selling price of the article to gain 20% should be Rs. 480.

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