The selling price of an article is Rs 21. The numerical value of loss percent and cost price is same. Find the cost price of the article.

Options

A. Rs 30
B. Rs 33
C. Rs 27
D. Rs 36

Answer

To solve the problem step by step, we will denote the Cost Price (CP) as \( x \) and the Selling Price (SP) as Rs. 21. We know that the loss percent is equal to the cost price.

### Step 1: Understand the relationship between SP, CP, and loss percent
The formula for selling price when there is a loss is given by:
\[ SP = CP \times \left(1 - \frac{\text{Loss Percent}}{100}\right) \]
Since the loss percent is equal to the cost price, we can denote the loss percent as \( x \).

### Step 2: Substitute the values into the formula
Given that \( SP = 21 \) and \( \text{Loss Percent} = x \):
\[ 21 = x \times \left(1 - \frac{x}{100}\right) \]

### Step 3: Rearranging the equation
Expanding the equation gives:
\[ 21 = x - \frac{x^2}{100} \]
Multiplying through by 100 to eliminate the fraction:
\[ 2100 = 100x - x^2 \]

### Step 4: Rearranging into standard quadratic form
Rearranging the equation:
\[ x^2 - 100x + 2100 = 0 \]

### Step 5: Factor the quadratic equation
To factor the quadratic equation, we look for two numbers that multiply to 2100 and add to -100. The numbers are -70 and -30:
\[ (x - 70)(x - 30) = 0 \]

### Step 6: Solve for \( x \)
Setting each factor to zero gives:
\[ x - 70 = 0 \quad \text{or} \quad x - 30 = 0 \]
Thus, \( x = 70 \) or \( x = 30 \).

### Step 7: Determine the valid cost price
Since the loss percent cannot exceed the cost price, we consider \( x = 30 \) as the valid solution. Therefore, the cost price of the article is Rs. 30.

### Final Answer
The cost price of the article is Rs. 30.

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