Ramesh bought a calculator with 20% discount on the tag-price. He obtained 10% profit by selling it for Rs 440. What was the tag-price?

Options

A. Rs500
B. Rs400
C. Rs480
D. Rs360

Answer

To find the tag price of the calculator that Ramesh bought, we can follow these steps:

### Step 1: Define the Tag Price
Let the tag price of the calculator be \( X \).

### Step 2: Calculate the Cost Price after Discount
Ramesh received a 20% discount on the tag price. Therefore, the cost price (CP) after the discount can be calculated as:
\[ \text{Cost Price} = X - 0.20X = 0.80X = \frac{4X}{5} \]

### Step 3: Understand Selling Price and Profit
Ramesh sold the calculator for Rs 440 and made a profit of 10%. The selling price (SP) can be expressed in terms of the cost price:
\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]
Given that the profit is 10% of the cost price, we can write:
\[ \text{Profit} = 0.10 \times \text{Cost Price} = 0.10 \times \frac{4X}{5} \]
Thus, the selling price can also be expressed as:
\[ \text{Selling Price} = \frac{4X}{5} + 0.10 \times \frac{4X}{5} = \frac{4X}{5} + \frac{0.4X}{5} = \frac{4X + 0.4X}{5} = \frac{4.4X}{5} \]

### Step 4: Set Up the Equation
Since we know that the selling price is Rs 440, we can set up the equation:
\[ \frac{4.4X}{5} = 440 \]

### Step 5: Solve for X (Tag Price)
To solve for \( X \), we can multiply both sides of the equation by 5:
\[ 4.4X = 440 \times 5 \]
Calculating the right side:
\[ 4.4X = 2200 \]
Now, divide both sides by 4.4:
\[ X = \frac{2200}{4.4} \]
Calculating the division:
\[ X = 500 \]

### Conclusion
The tag price of the calculator is Rs 500.

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