A man sold an article at a loss of 20% . If he sells the article for Rs 12 more, he would gained 10%. The cost price of the article is

Options

A. Rs 60
B. Rs 40
C. Rs 30
D. Rs 22

Answer

To solve the problem step by step, we will denote the cost price of the article as \( CP = x \).

### Step 1: Determine Selling Price at a 20% Loss
The selling price (SP) when the article is sold at a loss of 20% can be calculated using the formula:
\[ SP = CP - \text{Loss} \]
The loss is 20% of the cost price, which can be expressed as:
\[ \text{Loss} = \frac{20}{100} \times x = 0.2x \]
Thus, the selling price at a 20% loss is:
\[ SP = x - 0.2x = 0.8x \]

### Step 2: Determine Selling Price for a 10% Gain
If the man sells the article for Rs 12 more than the previous selling price, the new selling price (SP') can be expressed as:
\[ SP' = SP + 12 = 0.8x + 12 \]
To find the selling price that gives a 10% gain, we use the formula:
\[ SP' = CP + \text{Profit} \]
The profit is 10% of the cost price, which can be expressed as:
\[ \text{Profit} = \frac{10}{100} \times x = 0.1x \]
Thus, the selling price for a 10% gain is:
\[ SP' = x + 0.1x = 1.1x \]

### Step 3: Set Up the Equation
Now we have two expressions for the new selling price:
1. From the loss scenario: \( SP' = 0.8x + 12 \)
2. From the gain scenario: \( SP' = 1.1x \)

Setting these two expressions equal gives us:
\[ 0.8x + 12 = 1.1x \]

### Step 4: Solve for x
Rearranging the equation to isolate \( x \):
\[ 12 = 1.1x - 0.8x \]
\[ 12 = 0.3x \]
Now, divide both sides by 0.3 to find \( x \):
\[ x = \frac{12}{0.3} = 40 \]

### Conclusion
The cost price of the article is \( \text{Rs } 40 \).

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