Amit bought a laptop at a 25% discount on its marked price. If he paid ₹28,500 for the laptop, what was its marked price?
₹38,000
Marked Price Calculation Explained
This problem involves finding the original price (marked price) of an item before a discount was applied. We are given the final price Amit paid (the selling price) and the percentage discount offered.
Understanding the Terms
- Marked Price (MP): The price listed on the tag before any discounts.
- Discount: A reduction in price, calculated as a percentage of the marked price.
- Selling Price (SP): The final price paid by the customer after the discount is applied.
Formulating the Relationship
The relationship between Marked Price, Discount, and Selling Price is:
\(Selling Price = Marked Price - Discount Amount\)
The discount amount is calculated based on the marked price. In this case, the discount is 25% of the marked price.
\(Discount Amount = 25% of Marked Price\)
Using LaTeX notation:
\( \text{Discount Amount} = 0.25 \times \text{MP} \)Now, substitute this into the selling price formula:
\( \text{SP} = \text{MP} - (0.25 \times \text{MP}) \)Factor out the Marked Price (MP):
\( \text{SP} = \text{MP} \times (1 - 0.25) \) \( \text{SP} = \text{MP} \times 0.75 \)Calculating the Marked Price
We know Amit paid ₹28,500, which is the Selling Price (SP). We need to find the Marked Price (MP).
We can rearrange the formula to solve for MP:
\( \text{MP} = \frac{\text{SP}}{0.75} \)Substitute the given Selling Price:
\( \text{MP} = \frac{28500}{0.75} \)To perform the division, we can think of 0.75 as \(\frac{3}{4}\):
\( \text{MP} = \frac{28500}{3/4} \) \( \text{MP} = 28500 \times \frac{4}{3} \)First, divide 28500 by 3:
\( \frac{28500}{3} = 9500 \)Now, multiply the result by 4:
\( \text{MP} = 9500 \times 4 \) \( \text{MP} = 38000 \)So, the marked price of the laptop was ₹38,000.
Summary of Calculation Steps
- Identify the given Selling Price (SP) = ₹28,500.
- Identify the Discount Percentage = 25%.
- Understand that the Selling Price represents the remaining percentage after the discount: \(100\% - 25\% = 75\%\) of the Marked Price.
- Set up the equation: \(75\% \times \text{MP} = \text{SP}\) or \(0.75 \times \text{MP} = 28500\).
- Solve for MP: \(\text{MP} = \frac{28500}{0.75}\).
- Calculate the final value: MP = ₹38,000.
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