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
- 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?
- 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 _______.
- If a selling price of ₹36 results in a 10% discount on a list price, what selling price will result in a 20% discount on the list price?
- 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?
- A man got a discount of 10% on sugar at Big Mart which allowed him to buy 25 kg more for ₹225/-. What is the discounted price and the original price of the sugar per kg?
- Rahul bought a sweater and saved ₹200 when a discount of 25% was given. What was the price of the sweater before the discount?
- After deducting a commission of 10% on the marked price, a T.V. set costs ₹9,090. What is its marked price?
- A man purchased a fan which had a printed price of ₹200. If he received two successive discounts of 30% and 20%, then how much did he pay for the fan?
- Find a single discount equivalent to successive discounts of 5% and 20%.
Important Questions from Discount and MP
If a trader marks the price of an article 50 percent more than the cost price and allows a discount of 30 percent, then what is his profit percentage?
Printed price of a mobile is Rs. 6,400. It is sold in Rs. 2,560 with two consecutive discount. If first discount is 20%, then what is the second discount?
A trader decided to mark his goods 15 percent above the cost price and then offered 40 percent discount. What will be the percentage of profit or loss?
On the sale of 20 percent discount, the value of an item is Rs. 760. What was the real value of the item?
What is the total discount applicable if 3 successive discounts of 20%, 10% and 12.5% are applied?
