Understanding Profit and Discount Calculation
The problem involves calculating the profit percentage based on the relationship between profit and discount, and the given discount percentage.
Key Information Extraction
- Profit (P) is three times the Discount (D): $ P = 3D $
- Discount Percentage = 6.25%
Calculating Discount and Profit in Terms of Marked Price (MP)
First, convert the discount percentage to a fraction:
$ 6.25\% = \frac{6.25}{100} = \frac{625}{10000} = \frac{1}{16} $The discount (D) is calculated on the Marked Price (MP):
$ D = \frac{1}{16} \times \text{MP} $Using the relationship $ P = 3D $, we find the profit (P):
$ P = 3 \times \left( \frac{1}{16} \times \text{MP} \right) = \frac{3}{16} \times \text{MP} $Determining Selling Price (SP) and Cost Price (CP)
The Selling Price (SP) is the Marked Price (MP) minus the Discount (D):
$ \text{SP} = \text{MP} - D = \text{MP} - \frac{1}{16} \times \text{MP} = \frac{15}{16} \times \text{MP} $The Selling Price (SP) is also the Cost Price (CP) plus the Profit (P):
$ \text{SP} = \text{CP} + P $Substitute the expressions for SP and P in terms of MP:
$ \frac{15}{16} \times \text{MP} = \text{CP} + \frac{3}{16} \times \text{MP} $Now, solve for the Cost Price (CP) in terms of MP:
$ \text{CP} = \frac{15}{16} \times \text{MP} - \frac{3}{16} \times \text{MP} $ $ \text{CP} = \frac{12}{16} \times \text{MP} = \frac{3}{4} \times \text{MP} $Calculating the Profit Percentage
The profit percentage is calculated using the formula:
$ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 $Substitute the values of Profit (P) and Cost Price (CP) in terms of MP:
$ \text{Profit Percentage} = \left( \frac{\frac{3}{16} \times \text{MP}}{\frac{3}{4} \times \text{MP}} \right) \times 100 $Simplify the expression:
$ \text{Profit Percentage} = \left( \frac{3}{16} \times \frac{4}{3} \right) \times 100 $ $ \text{Profit Percentage} = \left( \frac{1}{4} \right) \times 100 $ $ \text{Profit Percentage} = 25\% $Important Questions from Profit & Loss (Notes)
- A person incurs a loss of 10% by selling a watch for Rs. 450. At what price should the watch be sold to earn 10% profit?
- A shopkeeper bought an item for ₹7825 and marked it at 30% higher than the cost price. If he sells the item by allowing 20% discount, then his profit percentage will be :
- A bought an article at a certain price and sold it at 10% profit. B bought the same article at a price 10% lesser than A and sold it at ₹18 lesser than A. B's gain percentage in this deal is 20%. At what price B bought the article?
- A dealer buys two articles X and Y for ₹500 each. He marks each of them at the same price. He sells X by giving two successive discounts of 50% and 28% and still earns ₹958 as profit. If he sells Y at a single discount of 77%, then what is the profit percentage on Y?
Restaurants A, B, C, and D give the following offers:
A: one mocktail free for every two purchased
B: one mocktail free for every three purchased
C: two mocktails free for every six purchased
D: 30% discount on each mocktail
If all of the restaurants have the same marked price for each mocktail, in which restaurant would you pay the least if you drank eight mocktails?
