A person sells an article at 21% discount and gets 21% profit on it, then find the ratio of cost price and marked price.

Options

A. 121 : 79
B. 79 : 121
C. 121 : 89
D. 132 : 99

Answer

To solve the problem step by step, we will find the ratio of the cost price (CP) to the marked price (MP) given that a person sells an article at a 21% discount and makes a 21% profit.

### Step-by-Step Solution:

1. **Assume Selling Price (SP)**:
Let's assume the selling price (SP) of the article is \( X \).

**Hint**: Start by defining a variable for the selling price to simplify calculations.

2. **Calculate Marked Price (MP)**:
Since the article is sold at a 21% discount, we can express the selling price in terms of the marked price:
\[ SP = MP - \text{Discount} \]
The discount is 21% of the marked price, so:
\[ X = MP - 0.21 \times MP = 0.79 \times MP \]

**Hint**: Use the relationship between selling price and marked price to find MP.

3. **Relate Selling Price to Cost Price (CP)**:
The person makes a 21% profit on the cost price. Thus, we can express the selling price in terms of cost price:
\[ SP = CP + \text{Profit} \]
The profit is 21% of the cost price, so:
\[ X = CP + 0.21 \times CP = 1.21 \times CP \]

**Hint**: Profit can be expressed as a percentage of cost price to relate SP and CP.

4. **Set the Two Expressions for SP Equal**:
Now we have two expressions for SP:
\[ 0.79 \times MP = 1.21 \times CP \]

**Hint**: Equate the two expressions to find a relationship between CP and MP.

5. **Rearranging the Equation**:
Rearranging the equation to find the ratio of CP to MP:
\[ \frac{CP}{MP} = \frac{0.79}{1.21} \]

**Hint**: Isolate CP and MP to find their ratio.

6. **Simplifying the Ratio**:
To express the ratio in a simpler form, we can multiply both the numerator and denominator by 100 to avoid decimals:
\[ \frac{CP}{MP} = \frac{79}{121} \]

**Hint**: Simplifying fractions can help in understanding the ratio better.

### Final Answer:
The ratio of the cost price to the marked price is:
\[ \frac{CP}{MP} = \frac{79}{121} \]