The selling price of an article is rs 228528. A shopkeeper marks its price 15% above its cost price and gives a discount of 10%. The cost price is :

Options

A. rs 2,18,650
B. rs 2,87,390
C. rs 2,8,740
D. rs 2,20,800

Answer

To solve the problem step by step, we will follow the given information and apply the formulas related to profit, loss, and discounts.

### Given:
- Selling Price (SP) = Rs 228,528
- Marked Price (MP) is 15% above Cost Price (CP)
- Discount = 10%

### Step 1: Calculate the effective selling price after discount
The selling price after a discount can be expressed as:
\[ SP = MP \times (1 - \text{Discount Rate}) \]

Given that the discount is 10%, we can express it as:
\[ SP = MP \times (1 - 0.10) = MP \times 0.90 \]

### Step 2: Substitute the selling price into the equation
Now, substituting the given selling price into the equation:
\[ 228528 = MP \times 0.90 \]

### Step 3: Solve for the Marked Price (MP)
To find MP, we rearrange the equation:
\[ MP = \frac{228528}{0.90} \]

Calculating this gives:
\[ MP = 254,020 \]

### Step 4: Relate the Marked Price to the Cost Price
Since the marked price is 15% above the cost price, we can express it as:
\[ MP = CP \times (1 + 0.15) = CP \times 1.15 \]

### Step 5: Substitute the Marked Price into the equation
Now, substituting the value of MP into the equation:
\[ 254020 = CP \times 1.15 \]

### Step 6: Solve for the Cost Price (CP)
To find CP, we rearrange the equation:
\[ CP = \frac{254020}{1.15} \]

Calculating this gives:
\[ CP = 220,017.39 \]

### Step 7: Round the Cost Price
Since cost price is generally expressed in whole numbers, we can round it to:
\[ CP \approx 220,017 \]

### Final Answer:
The cost price of the article is approximately Rs 220,017.

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