Cost price of 10 articles is equal to marked price of 8 articles and when shopkeeper sells an article at 20% discount then he earns Rs.48 less than the amount he earned when he sells an article at 12% discount. Find cost price of the article.

Options

A. Rs 560
B. Rs 540
C. Rs 420
D. Rs 480

Answer

To solve the problem step by step, let's define the variables and set up the equations based on the information provided.

### Step 1: Define Variables
Let:
- Cost Price (CP) of one article = \( x \)
- Marked Price (MP) of one article = \( y \)

### Step 2: Set Up the Equation for Cost Price and Marked Price
According to the problem, the cost price of 10 articles is equal to the marked price of 8 articles. Therefore, we can write the equation as:
\[ 10x = 8y \]
From this, we can express the marked price in terms of the cost price:
\[ y = \frac{10x}{8} = \frac{5x}{4} \]

### Step 3: Set Up the Selling Price Equations
When the shopkeeper sells an article at a 20% discount, the selling price (SP) is:
\[ SP_{20\%} = y - 0.2y = 0.8y \]
When he sells at a 12% discount, the selling price is:
\[ SP_{12\%} = y - 0.12y = 0.88y \]

### Step 4: Set Up the Profit Difference Equation
According to the problem, when selling at a 20% discount, he earns Rs. 48 less than when selling at a 12% discount. Therefore, we can write:
\[ SP_{12\%} - SP_{20\%} = 48 \]
Substituting the selling prices:
\[ 0.88y - 0.8y = 48 \]
This simplifies to:
\[ 0.08y = 48 \]

### Step 5: Solve for Marked Price
Now, we can solve for \( y \):
\[ y = \frac{48}{0.08} = 600 \]

### Step 6: Substitute Back to Find Cost Price
Now that we have the marked price, we can substitute back to find the cost price:
\[ y = \frac{5x}{4} \]
Substituting \( y = 600 \):
\[ 600 = \frac{5x}{4} \]
Multiplying both sides by 4:
\[ 2400 = 5x \]
Now, divide by 5:
\[ x = \frac{2400}{5} = 480 \]

### Conclusion
The cost price of one article is Rs. 480.

---