Aman purchased an article at a discount of 30% and sold it to Param at 40% profit. What is the ratio between the marked price and the price for which Param purchased the article?

Options

A. `10:9`
B. `15:14`
C. `25:24`
D. `50:49`

Answer

To solve the problem step by step, let's denote the marked price of the article as \( M \).

### Step 1: Determine the cost price for Aman after discount
Aman purchased the article at a discount of 30%. This means he paid 70% of the marked price.

\[ \text{Cost Price for Aman} = M \times (1 - 0.30) = M \times 0.70 \]

### Step 2: Calculate the selling price for Param
Aman sold the article to Param at a profit of 40%. The selling price (SP) can be calculated as follows:

\[ \text{Selling Price for Param} = \text{Cost Price for Aman} \times (1 + 0.40) = (M \times 0.70) \times 1.40 \]

Calculating this gives:

\[ \text{Selling Price for Param} = M \times 0.70 \times 1.40 = M \times 0.98 \]

### Step 3: Find the ratio between the marked price and the selling price for Param
Now we need to find the ratio of the marked price \( M \) to the selling price for Param \( (M \times 0.98) \).

\[ \text{Ratio} = \frac{M}{M \times 0.98} = \frac{1}{0.98} \]

### Step 4: Simplify the ratio
To simplify the ratio, we can express it as:

\[ \text{Ratio} = \frac{100}{98} = \frac{50}{49} \]

### Conclusion
The ratio between the marked price and the price for which Param purchased the article is \( 50:49 \).

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