A discount of 45% on an article is equal to the discount of 65% on other article. What is the respective ratio of the marked price of both the articles?

Options

A. `5:9`
B. `3:4 `
C. `7:12 `
D. `13:9`

Answer

To solve the problem, we need to find the respective ratio of the marked prices of two articles based on the given discounts.

Let:
- \( M_1 \) = Marked price of the first article
- \( M_2 \) = Marked price of the second article

According to the problem:
- A discount of 45% on the first article is equal to a discount of 65% on the second article.

This can be expressed mathematically as:
\[ 0.45 \times M_1 = 0.65 \times M_2 \]

Now, we can rearrange this equation to find the ratio of the marked prices \( M_1 \) and \( M_2 \):
\[ \frac{M_1}{M_2} = \frac{0.65}{0.45} \]

Next, we simplify the fraction \( \frac{0.65}{0.45} \):
\[ \frac{0.65}{0.45} = \frac{65}{45} \]

To simplify \( \frac{65}{45} \), we can divide both the numerator and the denominator by 5:
\[ \frac{65 \div 5}{45 \div 5} = \frac{13}{9} \]

Thus, the respective ratio of the marked prices of both articles is:
\[ M_1 : M_2 = 13 : 9 \]

### Final Answer:
The respective ratio of the marked price of both articles is \( 13 : 9 \).