The cost price of an article is Rs x. It is marked up by 200%. It is sold at Rs 5.40 after giving 25% discount. What is the value of x (in Rs)?

Options

A. 3.6
B. 2.5
C. 3
D. 2.4

Answer

To solve the problem step by step, we will follow the details given in the question.

### Step 1: Understand the Cost Price and Marked Price
The cost price (CP) of the article is given as Rs x. It is marked up by 200%.

**Hint:** Remember that a markup of 200% means the marked price (MP) is 300% of the cost price.

### Step 2: Calculate the Marked Price
Since the CP is Rs x, the marked price (MP) can be calculated as:
\[ MP = CP + (200\% \text{ of } CP) = x + 2x = 3x \]

**Hint:** To find the marked price, add the original cost price to the markup amount.

### Step 3: Understand the Selling Price and Discount
The article is sold for Rs 5.40 after giving a 25% discount on the marked price.

**Hint:** A discount of 25% means the selling price (SP) is 75% of the marked price.

### Step 4: Set Up the Equation for Selling Price
The selling price (SP) can be expressed in terms of the marked price:
\[ SP = MP - \text{Discount} = MP - (25\% \text{ of } MP) = MP \times (1 - 0.25) = MP \times 0.75 \]
Thus,
\[ 5.40 = 0.75 \times MP \]

**Hint:** Use the percentage to calculate the effective selling price after discount.

### Step 5: Substitute the Marked Price
Now substitute the expression for MP from Step 2 into the equation from Step 4:
\[ 5.40 = 0.75 \times (3x) \]

**Hint:** Replace MP with its equivalent expression to find the relationship between selling price and cost price.

### Step 6: Solve for x
Now we can solve for x:
\[ 5.40 = 2.25x \]
To find x, divide both sides by 2.25:
\[ x = \frac{5.40}{2.25} \]

**Hint:** When dividing, ensure you simplify the fraction correctly.

### Step 7: Calculate the Value of x
Calculating the division:
\[ x = \frac{5.40}{2.25} = 2.4 \]

**Hint:** Perform the division carefully to ensure accuracy.

### Conclusion
The value of x (the cost price) is Rs 2.4.

**Final Answer:** The cost price of the article is Rs 2.4.

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