Understanding the Problem
The question requires finding the discount percentage. The shopkeeper marks an item 40% above its cost price (CP) and wants to make a 26% profit.
Calculating Prices
Let the Cost Price (CP) be \(100\).
- Marked Price (MP): Calculated as CP plus 40% of CP. \( MP = CP \times (1 + 0.40) = 100 \times 1.40 = 140 \)
- Selling Price (SP): The desired profit is 26% of CP. \( SP = CP \times (1 + 0.26) = 100 \times 1.26 = 126 \)
Calculating Discount Percentage
The discount is applied to the Marked Price to get the Selling Price.
- Discount Amount: The difference between MP and SP. \( Discount = MP - SP = 140 - 126 = 14 \)
- Discount Percentage: Calculated as (Discount / MP) multiplied by 100%. \( Discount \% = \left ( \frac{Discount}{MP} \right ) \times 100\% \) \( Discount \% = \left ( \frac{14}{140} \right ) \times 100\% \) \( Discount \% = \frac{1}{10} \times 100\% = 10\% \)
The shopkeeper must offer a 10% discount.
Important Questions from Discount and MP
A single discount equivalent to two successive discounts of 15% and 25% is:
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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?
