Understanding Markup Percentage Calculation
The question asks for the percentage above the cost price (CP) a shopkeeper should mark goods (Marked Price, MP) to achieve a specific profit (Gain) after offering a discount.
- Let the Cost Price (CP) be $100$.
- The desired Gain is $12\%$.
- The Discount offered is $25\%$.
Calculating Markup Percentage
First, determine the Selling Price (SP) needed to achieve the desired gain.
Using the formula $SP = CP \times (1 + \frac{Gain\%}{100})$:
$SP = 100 \times (1 + \frac{12}{100})$ $SP = 100 \times (1 + 0.12)$ $SP = 100 \times 1.12$ $SP = 112$Next, find the Marked Price (MP) based on the Selling Price (SP) and the discount percentage.
The formula relating SP, MP, and Discount is $SP = MP \times (1 - \frac{Discount\%}{100})$.
$112 = MP \times (1 - \frac{25}{100})$ $112 = MP \times (1 - 0.25)$ $112 = MP \times 0.75$ $MP = \frac{112}{0.75}$ $MP = \frac{112}{3/4}$ $MP = 112 \times \frac{4}{3}$ $MP = \frac{448}{3}$Now, calculate the percentage markup above the cost price.
Markup Percentage $= \frac{MP - CP}{CP} \times 100$
Markup Percentage $= \frac{\frac{448}{3} - 100}{100} \times 100$ Markup Percentage $= (\frac{448}{3} - \frac{300}{3}) \%$ Markup Percentage $= \frac{148}{3} \%$ Markup Percentage $= 49 \frac{1}{3}\%$Therefore, the shopkeeper should mark the goods $49 \frac{1}{3}\%$ above the cost price.
Similar Questions
- An item marked for ₹38,800 is available on a discount of 25% or two successive discounts of 10% and 15%. What is the difference between the selling prices in the discount schemes?
- A wholesaler gives a scheme discount of 10% on a marked price of ₹400. What is the selling price?
- Find a single discount equivalent to successive discounts of 5% and 20%.
- Find a single discount equivalent to successive discounts of 15% and 18%.
- A dealer offers successive discounts of 15% and 12% on a refrigerator marked at ₹25,000. What is the final selling price?
- The marked price of a shirt is ₹500. If the shopkeeper offers a 20% discount, what is the selling price of the shirt?
- An article is marked for ₹720. If two successive discounts of 10% and 15% are allowed for sale, then the selling price of the article is:
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- If on a marked price, the difference between selling prices with a discount of 45% and two successive discounts of 30% and 20% is ₹84, then the marked price is _______.
- A salesman offers 20% additional discount, after offering an initial discount of 25% on the labelled rate of a laptop. If the final sale price of the laptop is ₹18,000, then what was its labelled rate?
Important Questions from Discount and MP
The marked price of an article is Rs. 1500. A shopkeeper sells it by giving 20% discount on its marked price. If the cost price of the article is Rs. 991, then his profit (in Rs.) is:
Surbhi sold an article for Rs. 176 after giving 12% discount on its marked price. Had she not given any discount; she would have earned a profit of 25%. What is the cost price (in Rs.) of the article?
The marked price of an article is Rs. 240. A shopkeeper sells it by allowing 18% discount on its marked price and still gains 23%. What is the cost price (in Rs.) of the article?
Three shopkeepers A, B and C marked on an identical article at Rs. 4820. A, B and C sold their article on successive discounts of 20% and 20%; 25% and 15%; 30% and 10% respectively. Which shopkeeper gives the maximum discount and how much (in Rs.)?
Find a single discount percentage equivalent to successive discounts of 10%, 20% and 25%.
