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.
Important Questions from Discount and MP
A single discount equivalent to two successive discounts of 15% and 25% is:
Ramesh purchases 75 articles for ₹ 10800 and sells them at a loss equal to the selling price of 5 articles. What will be the selling price of one article?
A TV was available for Rs. 14,500. The price came down to Rs. 11,890 during the Diwali sale. What is the percentage discount?
A shopkeeper marks the marked price of an article 30% more than its real price and offers 10% discount. What is the gain percentage?
An article was sold for Rs. 1,215 after giving a discount of 19%. If a discount of 17.5% is given, then for how much (in Rs.) should the article be sold?
