A shopkeeper sells an article at 14% discount on its marked price and still gains 20%. If the cost price of the article is 184.90, then what is its marked price?

Options

A. 264
B. 272
C. 278
D. 258

Answer

To find the marked price of the article, we can follow these steps:

### Step 1: Understand the relationship between cost price, selling price, and marked price.
The selling price (SP) can be calculated using the cost price (CP) and the profit percentage. The formula for selling price when profit is involved is:
\[ SP = CP + (Profit \% \times CP) \]

### Step 2: Calculate the selling price using the cost price and profit percentage.
Given:
- Cost Price (CP) = 184.90
- Profit Percentage = 20%

First, we calculate the profit:
\[ Profit = 20\% \text{ of } 184.90 = \frac{20}{100} \times 184.90 = 36.98 \]

Now, we can find the selling price:
\[ SP = CP + Profit = 184.90 + 36.98 = 221.88 \]

### Step 3: Relate the selling price to the marked price using the discount.
The selling price is also related to the marked price (MP) through the discount given. The formula is:
\[ SP = MP - (Discount \% \times MP) \]

Given:
- Discount Percentage = 14%

This can be rewritten as:
\[ SP = MP \times (1 - \frac{Discount \%}{100}) \]
\[ SP = MP \times (1 - 0.14) = MP \times 0.86 \]

### Step 4: Substitute the selling price into the equation and solve for the marked price.
We already calculated the selling price (SP) as 221.88. Now we can set up the equation:
\[ 221.88 = MP \times 0.86 \]

To find the marked price (MP), we rearrange the equation:
\[ MP = \frac{221.88}{0.86} \]

### Step 5: Calculate the marked price.
Now, performing the division:
\[ MP = \frac{221.88}{0.86} \approx 258.00 \]

Thus, the marked price of the article is approximately **258.00**.

### Summary of Steps:
1. Calculate the selling price using the cost price and profit percentage.
2. Relate the selling price to the marked price using the discount percentage.
3. Substitute the selling price into the equation and solve for the marked price.