The value of discount of 18% on first article is equal to the value of discount of 13% on second article. What is the ratio of the marked price of two articles?

Options

A. `17:24 `
B. ` 39:50 `
C. ` 13:18 `
D. `13:19 `

Answer

To find the ratio of the marked prices of the two articles based on the given discounts, we can follow these steps:

### Step 1: Understand the given information
We know that the value of the discount on the first article (18%) is equal to the value of the discount on the second article (13%).

### Step 2: Set up the equation
Let the marked price of the first article be \( A \) and the marked price of the second article be \( B \). The discounts can be expressed as:
- Discount on first article = \( 18\% \) of \( A = \frac{18}{100} \times A \)
- Discount on second article = \( 13\% \) of \( B = \frac{13}{100} \times B \)

According to the problem, these two discounts are equal:
\[ \frac{18}{100} \times A = \frac{13}{100} \times B \]

### Step 3: Simplify the equation
We can eliminate the \( \frac{1}{100} \) from both sides:
\[ 18A = 13B \]

### Step 4: Rearrange the equation to find the ratio
To find the ratio of \( A \) to \( B \), we can rearrange the equation:
\[ \frac{A}{B} = \frac{13}{18} \]

### Step 5: State the final answer
Thus, the ratio of the marked prices of the two articles is:
\[ A : B = 13 : 18 \]