Calculate Marked Price from Selling Price and Discounts
The shopkeeper sells the item for ₹225.6 after applying two successive discounts: 90% and 50%. We first need to find the marked price (MP).
- The effective selling price after a 90% discount is \((100\% - 90\%) = 10\%\) of the marked price.
- The second discount of 50% is applied to this reduced price. So, the final selling price is \((100\% - 50\%) = 50\%\) of the price after the first discount.
- Mathematically, the selling price (SP) can be represented as: \(SP = MP \times (1 - \text{Discount}_1) \times (1 - \text{Discount}_2)\) \(SP = MP \times (1 - 0.90) \times (1 - 0.50)\) \(SP = MP \times 0.10 \times 0.50\) \(SP = MP \times 0.05\)
- Given \(SP = ₹225.6\): \(₹225.6 = MP \times 0.05\)
- Solving for MP: \(MP = \frac{₹225.6}{0.05} = ₹4512\)
Determine Cost Price Using Marked Price and Profit
If no discount were given, the selling price would equal the marked price (\(MP = ₹4512\)). In this scenario, the shopkeeper would earn a profit of 41%.
- The relationship between Marked Price (MP), Cost Price (CP), and Profit Percentage is: \(MP = CP \times (1 + \text{Profit Percentage})\)
- Given Profit Percentage = 41% or 0.41: \(MP = CP \times (1 + 0.41)\) \(MP = CP \times 1.41\)
- Substitute the calculated MP value: \(₹4512 = CP \times 1.41\)
- Solving for CP: \(CP = \frac{₹4512}{1.41}\) \(CP = ₹3200\)
Therefore, the cost price of the item is ₹3,200.
Similar Questions
- Two successive discounts of 25% and 10% on a deal are equivalent to a single discount of:
- An article was sold for ₹2,500. Had a discount of 10% been offered, a profit of 12.5% would have been made. What was the cost price?
In a clearance sale of electronic items, an item whose marked price was ₹12,225 is now sold for ₹10,756. d% is the discount percentage on the item. The value of d is:
The list price of an article is ₹5,000 and a discount of 70% is offered on the list price. What additional discount per cent on the already discounted price must be offered to a customer to bring the net selling price to ₹1,275?
The cost price of a toy is ₹210. What should be its marked price so that, after a discount of 5%, the shopkeeper gains 90%?
A scheme like 'Buy 5, Get 6' on the same kind of articles with the same marked price offers a _______ discount.
- The list price of an article is ₹5,100 and a discount of 32% is offered on the list price. What additional discount per cent on the already discounted price must be offered to a customer to bring the net selling price to ₹1,734?
Two successive discounts of 10% and 5% are equivalent to a single discount of______.
- A product, whose MRP is ₹1,590, is sold for ₹835 by a wholesale shop owner. What is the percentage of discount given by him (nearest to its integer)?
Two successive discounts of 40% and 60% on a deal equivalent to a single discount of:
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?
