A shopkeeper marks an article `24%` above its cost price and allows a `15%` discount on the marked price. If he earns a profit of 27 by selling the article, then the selling price of the article is :

Options

A. Rs 508
B. Rs 522
C. Rs 517
D. Rs 527

Answer

To solve the problem step by step, we will denote the cost price (CP) of the article as \( CP \).

### Step 1: Calculate the Marked Price (MP)
The marked price is 24% above the cost price. Therefore, we can express the marked price as:
\[ MP = CP + 0.24 \times CP = 1.24 \times CP \]

### Step 2: Calculate the Selling Price (SP) after Discount
The shopkeeper allows a 15% discount on the marked price. The selling price after applying the discount can be calculated as:
\[ SP = MP - 0.15 \times MP = MP \times (1 - 0.15) = MP \times 0.85 \]
Substituting the expression for MP from Step 1:
\[ SP = (1.24 \times CP) \times 0.85 = 1.054 \times CP \]

### Step 3: Relate Selling Price to Profit
The shopkeeper earns a profit of 27. This means that the selling price is equal to the cost price plus the profit:
\[ SP = CP + 27 \]

### Step 4: Set the Two Expressions for SP Equal
Now we have two expressions for SP:
1. \( SP = 1.054 \times CP \)
2. \( SP = CP + 27 \)

Setting them equal to each other:
\[ 1.054 \times CP = CP + 27 \]

### Step 5: Solve for CP
Now, we will solve for CP:
\[ 1.054 \times CP - CP = 27 \]
\[ (1.054 - 1) \times CP = 27 \]
\[ 0.054 \times CP = 27 \]
\[ CP = \frac{27}{0.054} = 500 \]

### Step 6: Calculate the Selling Price
Now that we have the cost price, we can find the selling price using either expression for SP. Using \( SP = CP + 27 \):
\[ SP = 500 + 27 = 527 \]

Thus, the selling price of the article is \( \text{SP} = 527 \).

### Final Answer
The selling price of the article is **527**.

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