Rohan sells two articles. The cost price of the first article is equal to the selling price of the second article. The first article is sold at a profit of 40% and the second article is sold at a loss of 40%. What is the ratio of the selling price of the first article to the cost price of the second article?

Options

A. `21:25`
B. `25:21`
C. `30:29`
D. `29:30`

Answer

To solve the problem step by step, we will define the variables and use the information given in the question.

### Step 1: Define the Cost Price (CP) and Selling Price (SP)
Let the cost price of the first article be \( CP_1 \) and the selling price of the first article be \( SP_1 \). Similarly, let the cost price of the second article be \( CP_2 \) and the selling price of the second article be \( SP_2 \).

### Step 2: Set up the relationships
According to the problem:
1. The first article is sold at a profit of 40%. Therefore, we can express the selling price of the first article as:
\[ SP_1 = CP_1 + 0.4 \times CP_1 = 1.4 \times CP_1 \]

2. The second article is sold at a loss of 40%. Therefore, we can express the selling price of the second article as:
\[ SP_2 = CP_2 - 0.4 \times CP_2 = 0.6 \times CP_2 \]

3. The cost price of the first article is equal to the selling price of the second article:
\[ CP_1 = SP_2 \]

### Step 3: Substitute the expressions
From the relationship established in Step 2, we can substitute \( SP_2 \):
\[ CP_1 = 0.6 \times CP_2 \]

### Step 4: Express \( SP_1 \) in terms of \( CP_2 \)
Now, substituting \( CP_1 \) in the expression for \( SP_1 \):
\[ SP_1 = 1.4 \times CP_1 = 1.4 \times (0.6 \times CP_2) = 0.84 \times CP_2 \]

### Step 5: Find the ratio of \( SP_1 \) to \( CP_2 \)
We need to find the ratio of the selling price of the first article to the cost price of the second article:
\[ \text{Ratio} = \frac{SP_1}{CP_2} = \frac{0.84 \times CP_2}{CP_2} = 0.84 \]

### Step 6: Convert the ratio to a fraction
To express 0.84 as a fraction, we can write:
\[ 0.84 = \frac{84}{100} = \frac{21}{25} \]

### Final Answer
Thus, the ratio of the selling price of the first article to the cost price of the second article is:
\[ \boxed{21:25} \]