If an article is sold at a gain of 5 % instead of being sold at a loss of 5%, a man gets Rs.5 more. What is the cost price of the article?

Options

A. Rs.50
B. Rs.40
C. Rs.60
D. Rs.80

Answer

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

### Step 1: Define the Cost Price
Let the cost price (CP) of the article be \( x \).

### Step 2: Calculate Selling Price at 5% Gain
The selling price (SP) when sold at a gain of 5% is calculated using the formula:
\[ SP = CP \times \left(1 + \frac{\text{Gain \%}}{100}\right) \]
Substituting the values, we get:
\[ SP_{\text{gain}} = x \times \left(1 + \frac{5}{100}\right) = x \times \frac{105}{100} = \frac{105x}{100} \]

### Step 3: Calculate Selling Price at 5% Loss
The selling price (SP) when sold at a loss of 5% is calculated using the formula:
\[ SP = CP \times \left(1 - \frac{\text{Loss \%}}{100}\right) \]
Substituting the values, we get:
\[ SP_{\text{loss}} = x \times \left(1 - \frac{5}{100}\right) = x \times \frac{95}{100} = \frac{95x}{100} \]

### Step 4: Set Up the Equation
According to the problem, the difference between the selling price at a gain of 5% and the selling price at a loss of 5% is Rs. 5. Therefore, we can write the equation:
\[ SP_{\text{gain}} - SP_{\text{loss}} = 5 \]
Substituting the values we calculated:
\[ \frac{105x}{100} - \frac{95x}{100} = 5 \]

### Step 5: Simplify the Equation
Now, simplify the left side:
\[ \frac{105x - 95x}{100} = 5 \]
This simplifies to:
\[ \frac{10x}{100} = 5 \]

### Step 6: Solve for x
To isolate \( x \), multiply both sides by 100:
\[ 10x = 500 \]
Now, divide both sides by 10:
\[ x = 50 \]

### Conclusion
The cost price of the article is Rs. 50.

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