By selling an article at 3/4th of the marked price, there is a gain of 25%. The ratio of the marked price and the cost price is

Options

A. `5:3`
B. `3:5`
C. `3:4`
D. `4:3`

Answer

To solve the problem step by step, let's denote the following:

- Let the marked price (MP) of the article be \( x \) rupees.
- The selling price (SP) is given as \( \frac{3}{4} \) of the marked price, which can be expressed as:
\[ SP = \frac{3}{4}x \]

- We are also given that there is a gain of 25%. The cost price (CP) can be calculated using the formula for gain:
\[ SP = CP + \text{Gain} \]
Since the gain is 25%, we can express the selling price in terms of cost price:
\[ SP = CP \times \left(1 + \frac{25}{100}\right) = CP \times \frac{125}{100} = CP \times \frac{5}{4} \]

- Setting the two expressions for SP equal to each other:
\[ \frac{3}{4}x = CP \times \frac{5}{4} \]

- To find the cost price (CP), we can rearrange the equation:
\[ CP = \frac{3}{4}x \times \frac{4}{5} = \frac{3}{5}x \]

- Now, we need to find the ratio of the marked price (MP) to the cost price (CP):
\[ \text{Ratio} = \frac{MP}{CP} = \frac{x}{\frac{3}{5}x} \]

- Simplifying the ratio:
\[ \text{Ratio} = \frac{x}{\frac{3}{5}x} = \frac{5}{3} \]

Thus, the ratio of the marked price to the cost price is \( 5:3 \).

### Final Answer:
The ratio of the marked price to the cost price is \( 5:3 \).