Table Lamp Profit Calculation: Understanding Selling Price

This problem involves calculating the Selling Price (SP) of a table lamp given the difference between the Cost Price (CP) and Selling Price (SP), and the profit percentage.

Key Information Given

• Difference between Selling Price and Cost Price (Profit) = ₹540
• Profit Percentage = 30%

Understanding Profit Percentage

Profit percentage is typically calculated based on the Cost Price (CP). The formula is:

Profit % = (Profit / CP) * 100

In this case, the profit is given as ₹540, and the profit percentage is 30%. We can use this to find the Cost Price.

Calculating the Cost Price (CP)

We know that the profit (₹540) is 30% of the Cost Price (CP).

Let the Cost Price be CP.

Using the profit percentage formula:

30% of CP = Profit

$$ \frac{30}{100} \times CP = 540 $$

To find CP, we rearrange the equation:

$$ CP = \frac{540 \times 100}{30} $$

$$ CP = 18 \times 100 $$

$$ CP = 1800 $$

So, the Cost Price of the table lamp is ₹1800.

Calculating the Selling Price (SP)

The Selling Price is the Cost Price plus the Profit.

SP = CP + Profit

We have calculated the CP as ₹1800 and the profit is given as ₹540.

$$ SP = 1800 + 540 $$

$$ SP = 2340 $$

Therefore, the Selling Price of the table lamp is ₹2340.

Alternative Method: Using SP Percentage

If the profit is 30%, the Selling Price is 100% (Cost Price) + 30% (Profit) = 130% of the Cost Price.

The difference between the Selling Price and Cost Price is the Profit, which is 30% of the Cost Price.

We are given this difference (Profit) is ₹540.

$$ 30\% \text{ of } CP = 540 $$

$$ CP = \frac{540 \times 100}{30} = 1800 $$

Now, calculate the Selling Price:

$$ SP = 130\% \text{ of } CP $$

$$ SP = \frac{130}{100} \times 1800 $$

$$ SP = 130 \times 18 $$

$$ SP = 2340 $$

Both methods confirm that the Selling Price is ₹2340.

Summary Table