Calculating Cost Price with Discount and Profit
This solution finds the Cost Price (CP) using the information about a hypothetical discount and profit scenario. We interpret the initial selling price, ₹2,500, as the Marked Price (MP) for the calculation.
Step 1: Calculate Hypothetical Selling Price
First, find the Selling Price (SP) that would occur if a 10% discount was applied to the Marked Price (MP).
- Marked Price (MP) = ₹2,500
- Discount Rate = 10% or $0.10$
- Using the formula \(SP = MP \times (1 - \text{Discount Rate})\):
- \(SP = ₹2,500 \times (1 - 0.10)\)
- \(SP = ₹2,500 \times 0.90\)
- \(SP = ₹2,250\)
This calculated SP of ₹2,250 is the price at which a 12.5% profit would be made.
Step 2: Calculate Cost Price
Now, use the hypothetical Selling Price and the given profit percentage to calculate the Cost Price (CP).
- Hypothetical Selling Price (SP) = ₹2,250
- Profit Rate = 12.5% or $0.125$
- Using the formula \(SP = CP \times (1 + \text{Profit Rate})\):
- \(₹2,250 = CP \times (1 + 0.125)\)
- \(₹2,250 = CP \times 1.125\)
- Rearranging to solve for CP: \(CP = \frac{₹2,250}{1.125}\)
- \(CP = ₹2,000\)
The Cost Price of the article is ₹2,000.
Similar Questions
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Important Questions from Discount and MP
- Two successive discounts of 25% and 10% on a deal are equivalent to a single discount of:
- A shopkeeper offers the following three schemes. Which scheme has the maximum discount percent?
I. Two successive discounts of 15% and 20%.
II. Buy 4 get 2 free.
III. Buy 6 get 4 free - A shopkeeper is given a 10% trade discount and a 5% scheme discount (free units). On purchasing 100 units priced at ₹50 each, what is the trade discount amount?
- What is the equivalent single discount for successive discounts of 20% and 10%?
- Rahul buys a box of pens (listed price of ₹900) with a trade discount of 30%. What is the net price?
